Finite Group DatabasebetaFinite Group DatabasebetaOrder 3456.
696 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 696 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| # | subgroup | G/H | class size | multiplicity | normal? | properties |
|---|---|---|---|---|---|---|
| 1 | C23×PSU(3,𝔽2)⋊C3 | C2 | 1 | 1 | yes | maximal, characteristic |
| 2 | C2×(PSU(3,𝔽2)⋊C3)⋊C4 | C2 | 1 | 2 | yes | maximal, complemented |
| 3 | #11784747 | — | 3 | 1 | no | maximal |
| 4 | C22×PSU(3,𝔽2)⋊C3 | — | 2 | 2 | no | — |
| 5 | C22×PSU(3,𝔽2)⋊C3 | C4 | 1 | 2 | yes | complemented |
| 6 | C22×PSU(3,𝔽2)⋊C3 | C22 | 1 | 1 | yes | characteristic |
| 7 | (PSU(3,𝔽2)⋊C3)⋊C4 | — | 2 | 2 | no | — |
| 8 | #11721310 | — | 4 | 1 | no | maximal |
| 9 | C23×PSU(3,𝔽2) | D3 | 1 | 1 | yes | characteristic |
| 10 | C2×C22⋊AGL(1,𝔽9) | — | 3 | 1 | no | — |
| 11 | C2×PSU(3,𝔽2)⋊C4 | — | 3 | 2 | no | — |
| 12 | C2×PSU(3,𝔽2)⋊C4 | — | 3 | 2 | no | — |
| 13 | #10593516 | — | 3 | 1 | no | — |
| 14 | C2×PSU(3,𝔽2)⋊C3 | — | 2 | 2 | no | — |
| 15 | C2×PSU(3,𝔽2)⋊C3 | C2×C4 | 1 | 1 | yes | characteristic |
| 16 | C2×PSU(3,𝔽2)⋊C3 | D4 | 1 | 2 | yes | — |
| 17 | C23×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 18 | C2×((C3⋊D3)⋊C3)⋊C4 | — | 4 | 2 | no | — |
| 19 | #88552 | — | 4 | 1 | no | — |
| 20 | #3757⋊C3 | — | 4 | 1 | no | — |
| 21 | #88450 | — | 4 | 2 | no | — |
| 22 | #73148 | — | 9 | 1 | no | maximal |
| 23 | C23×#157 | — | 3 | 1 | no | — |
| 24 | C22×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 25 | C22×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 26 | C22×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 27 | C22×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 28 | C22×PSU(3,𝔽2) | Dic3 | 1 | 2 | yes | complemented |
| 29 | C22×PSU(3,𝔽2) | C2×D3 | 1 | 1 | yes | characteristic |
| 30 | C22×AGL(1,𝔽9) | — | 3 | 2 | no | — |
| 31 | C2×#3773 | — | 3 | 2 | no | — |
| 32 | C22⋊AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 33 | PSU(3,𝔽2)⋊C4 | — | 6 | 2 | no | — |
| 34 | PSU(3,𝔽2)⋊C4 | — | 6 | 4 | no | — |
| 35 | PSU(3,𝔽2)⋊C4 | — | 6 | 2 | no | — |
| 36 | #63974 | — | 6 | 1 | no | — |
| 37 | D3×#217 | — | 12 | 1 | no | — |
| 38 | #63737 | — | 6 | 1 | no | — |
| 39 | PSU(3,𝔽2)⋊C3 | C22⋊C4 | 1 | 1 | yes | characteristic, complemented |
| 40 | C23×H(3,𝔽3) | — | 4 | 1 | no | — |
| 41 | C22×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 42 | C22×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 43 | C22×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 44 | C22×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 45 | C22×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 46 | C22×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 47 | C2×#1084 | — | 4 | 2 | no | — |
| 48 | C2×(C3⋊Dic3)⋊C3 | — | 4 | 2 | no | — |
| 49 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 2 | no | — |
| 50 | ((C3⋊D3)⋊C3)⋊C4 | — | 8 | 2 | no | — |
| 51 | C23×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 52 | C2×#859 | — | 9 | 2 | no | — |
| 53 | C23×C3⋊D3 | S4 | 1 | 1 | yes | characteristic |
| 54 | C23×C3×D3 | — | 12 | 1 | no | — |
| 55 | C22×#157 | — | 3 | 1 | no | — |
| 56 | C22×#157 | — | 3 | 2 | no | — |
| 57 | C22×#157 | — | 3 | 2 | no | — |
| 58 | C22×#157 | — | 3 | 1 | no | — |
| 59 | C22×#157 | — | 6 | 2 | no | — |
| 60 | C22×#157 | — | 6 | 2 | no | — |
| 61 | C2×PSU(3,𝔽2) | — | 2 | 2 | no | — |
| 62 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 63 | C2×PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 64 | C2×PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 65 | C2×PSU(3,𝔽2) | — | 3 | 4 | no | — |
| 66 | C2×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 67 | C2×PSU(3,𝔽2) | — | 6 | 4 | no | — |
| 68 | C2×PSU(3,𝔽2) | — | 6 | 4 | no | — |
| 69 | C2×PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 70 | C2×PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 71 | C2×PSU(3,𝔽2) | C2×Dic3 | 1 | 1 | yes | characteristic |
| 72 | C2×PSU(3,𝔽2) | #67 | 1 | 2 | yes | — |
| 73 | C2×AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 74 | C2×AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 75 | C2×AGL(1,𝔽9) | — | 6 | 2 | no | — |
| 76 | C2×#624 | — | 6 | 2 | no | — |
| 77 | C2×D3×Dic3 | — | 12 | 2 | no | — |
| 78 | #3773 | — | 6 | 2 | no | — |
| 79 | #3773 | — | 6 | 2 | no | — |
| 80 | #3757 | — | 4 | 1 | no | — |
| 81 | C3×#217 | — | 12 | 1 | no | — |
| 82 | C3×#217 | — | 12 | 1 | no | — |
| 83 | C3×#217 | — | 24 | 1 | no | — |
| 84 | #3722 | — | 12 | 1 | no | — |
| 85 | (C2×D3)⋊Dic3 | — | 12 | 2 | no | — |
| 86 | #1787 | — | 27 | 1 | no | Sylow |
| 87 | C22×H(3,𝔽3) | — | 4 | 1 | no | — |
| 88 | C22×H(3,𝔽3) | — | 4 | 2 | no | — |
| 89 | C22×H(3,𝔽3) | — | 8 | 2 | no | — |
| 90 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 91 | C2×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 92 | C2×(C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 93 | C2×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 94 | C2×(C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 95 | C2×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 96 | C2×(C3⋊D3)⋊C3 | — | 8 | 4 | no | — |
| 97 | C2×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 98 | C2×(C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 99 | #1084 | — | 8 | 2 | no | — |
| 100 | (C3⋊Dic3)⋊C3 | — | 8 | 2 | no | — |
| 101 | C22×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 102 | C22×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 103 | C22×SL(2,𝔽3) | — | 18 | 2 | no | — |
| 104 | C2×#217 | — | 36 | 1 | no | — |
| 105 | D3×C22⋊C4 | — | 36 | 1 | no | — |
| 106 | #859 | — | 18 | 2 | no | — |
| 107 | C23×C32 | — | 4 | 1 | no | — |
| 108 | C23×C32 | — | 8 | 1 | no | — |
| 109 | C23×C32 | GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 110 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 111 | C22×C3⋊D3 | — | 2 | 2 | no | — |
| 112 | C22×C3⋊D3 | #226 | 1 | 2 | yes | — |
| 113 | C22×C3⋊D3 | GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 114 | C22×C3⋊D3 | SL(2,ℤ/4) | 1 | 2 | yes | — |
| 115 | C22×C3⋊D3 | C2×S4 | 1 | 1 | yes | characteristic |
| 116 | C22×C3×D3 | — | 12 | 1 | no | — |
| 117 | C22×C3×D3 | — | 12 | 2 | no | — |
| 118 | C22×C3×D3 | — | 12 | 2 | no | — |
| 119 | C22×C3×D3 | — | 12 | 1 | no | — |
| 120 | C22×C3×D3 | — | 24 | 2 | no | — |
| 121 | C22×C3×D3 | — | 24 | 2 | no | — |
| 122 | C2×#157 | — | 3 | 1 | no | — |
| 123 | C2×#157 | — | 3 | 1 | no | — |
| 124 | C2×#157 | — | 3 | 2 | no | — |
| 125 | C2×#157 | — | 3 | 2 | no | — |
| 126 | C2×#157 | — | 3 | 2 | no | — |
| 127 | C2×#157 | — | 6 | 2 | no | — |
| 128 | C2×#157 | — | 6 | 4 | no | — |
| 129 | C2×#157 | — | 6 | 2 | no | — |
| 130 | C2×#157 | — | 6 | 2 | no | — |
| 131 | PSU(3,𝔽2) | — | 3 | 1 | no | — |
| 132 | PSU(3,𝔽2) | — | 3 | 2 | no | — |
| 133 | PSU(3,𝔽2) | — | 3 | 4 | no | — |
| 134 | PSU(3,𝔽2) | — | 6 | 1 | no | — |
| 135 | PSU(3,𝔽2) | — | 6 | 2 | no | — |
| 136 | PSU(3,𝔽2) | — | 6 | 4 | no | — |
| 137 | PSU(3,𝔽2) | #217 | 1 | 1 | yes | characteristic, complemented |
| 138 | AGL(1,𝔽9) | — | 12 | 2 | no | — |
| 139 | C2×C3⋊Dic3 | — | 4 | 2 | no | — |
| 140 | C2×C3×Dic3 | — | 12 | 2 | no | — |
| 141 | C2×C3×Dic3 | — | 12 | 2 | no | — |
| 142 | C2×C3×Dic3 | — | 24 | 2 | no | — |
| 143 | #624 | — | 12 | 2 | no | — |
| 144 | #624 | — | 12 | 2 | no | — |
| 145 | D3×Dic3 | — | 24 | 2 | no | — |
| 146 | D3×Dic3 | — | 24 | 2 | no | — |
| 147 | C23×Q8 | — | 9 | 1 | no | — |
| 148 | C2×#103 | — | 27 | 2 | no | — |
| 149 | C2×#103 | — | 27 | 2 | no | — |
| 150 | C2×C22⋊C8 | — | 27 | 1 | no | — |
| 151 | #380 | — | 27 | 1 | no | — |
| 152 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 153 | C2×H(3,𝔽3) | — | 4 | 2 | no | — |
| 154 | C2×H(3,𝔽3) | — | 8 | 2 | no | — |
| 155 | (C3⋊D3)⋊C3 | — | 4 | 2 | no | — |
| 156 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 157 | (C3⋊D3)⋊C3 | — | 4 | 1 | no | — |
| 158 | (C3⋊D3)⋊C3 | — | 8 | 2 | no | — |
| 159 | C24×C3 | — | 36 | 1 | no | — |
| 160 | C23×D3 | — | 12 | 1 | no | — |
| 161 | C22×Dic3 | — | 36 | 2 | no | — |
| 162 | C2×C4×D3 | — | 36 | 2 | no | — |
| 163 | C2×SL(2,𝔽3) | — | 9 | 1 | no | — |
| 164 | C2×SL(2,𝔽3) | — | 9 | 2 | no | — |
| 165 | C2×SL(2,𝔽3) | — | 18 | 2 | no | — |
| 166 | C3×C22⋊C4 | — | 36 | 1 | no | — |
| 167 | #217 | — | 12 | 1 | no | — |
| 168 | #217 | — | 12 | 1 | no | — |
| 169 | #217 | — | 24 | 1 | no | — |
| 170 | #217 | — | 36 | 1 | no | — |
| 171 | #217 | — | 36 | 2 | no | — |
| 172 | (C2×D3)⋊C4 | — | 36 | 2 | no | — |
| 173 | C22×C32 | — | 2 | 2 | no | — |
| 174 | C22×C32 | — | 4 | 1 | no | — |
| 175 | C22×C32 | — | 4 | 2 | no | — |
| 176 | C22×C32 | — | 8 | 1 | no | — |
| 177 | C22×C32 | — | 8 | 2 | no | — |
| 178 | C22×C32 | — | 8 | 2 | no | — |
| 179 | C22×C32 | — | 16 | 2 | no | — |
| 180 | C22×C32 | #859 | 1 | 2 | yes | complemented |
| 181 | C22×C32 | C2×GL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 182 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 183 | C2×C3⋊D3 | — | 2 | 4 | no | — |
| 184 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 185 | C2×C3⋊D3 | — | 2 | 2 | no | — |
| 186 | C2×C3⋊D3 | #859 | 1 | 2 | yes | complemented |
| 187 | C2×C3⋊D3 | C2×#226 | 1 | 1 | yes | characteristic |
| 188 | C2×C3⋊D3 | #983 | 1 | 2 | yes | — |
| 189 | C2×C3⋊D3 | C2×SL(2,ℤ/4) | 1 | 1 | yes | characteristic |
| 190 | C2×C3⋊D3 | GL(2,ℤ/4) | 1 | 2 | yes | — |
| 191 | C2×C3×D3 | — | 12 | 2 | no | — |
| 192 | C2×C3×D3 | — | 12 | 2 | no | — |
| 193 | C2×C3×D3 | — | 12 | 1 | no | — |
| 194 | C2×C3×D3 | — | 12 | 1 | no | — |
| 195 | C2×C3×D3 | — | 12 | 2 | no | — |
| 196 | C2×C3×D3 | — | 24 | 4 | no | — |
| 197 | C2×C3×D3 | — | 24 | 2 | no | — |
| 198 | C2×C3×D3 | — | 24 | 2 | no | — |
| 199 | C2×C3×D3 | — | 24 | 2 | no | — |
| 200 | #157 | — | 3 | 2 | no | — |
| 201 | #157 | — | 3 | 1 | no | — |
| 202 | #157 | — | 3 | 1 | no | — |
| 203 | #157 | — | 6 | 2 | no | — |
| 204 | C3⋊Dic3 | — | 8 | 2 | no | — |
| 205 | C3×Dic3 | — | 24 | 2 | no | — |
| 206 | C3×Dic3 | — | 24 | 2 | no | — |
| 207 | C3×Dic3 | — | 48 | 2 | no | — |
| 208 | C22×Q8 | — | 9 | 1 | no | — |
| 209 | C22×Q8 | — | 9 | 2 | no | — |
| 210 | C22×Q8 | — | 18 | 2 | no | — |
| 211 | C22×Q8 | — | 27 | 1 | no | — |
| 212 | C22×Q8 | — | 27 | 2 | no | — |
| 213 | C22×Q8 | — | 54 | 2 | no | — |
| 214 | C23×C4 | — | 27 | 1 | no | — |
| 215 | C22×C8 | — | 27 | 2 | no | — |
| 216 | C2×C4⋊C4 | — | 27 | 2 | no | — |
| 217 | C2×C22⋊C4 | — | 54 | 1 | no | — |
| 218 | #103 | — | 54 | 2 | no | — |
| 219 | #103 | — | 54 | 2 | no | — |
| 220 | #103 | — | 54 | 4 | no | — |
| 221 | C22⋊C8 | — | 54 | 2 | no | — |
| 222 | #95 | — | 54 | 1 | no | — |
| 223 | H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 224 | C23×C3 | — | 4 | 1 | no | — |
| 225 | C23×C3 | — | 12 | 1 | no | — |
| 226 | C23×C3 | — | 24 | 1 | no | — |
| 227 | C23×C3 | — | 36 | 1 | no | — |
| 228 | C23×C3 | — | 36 | 1 | no | — |
| 229 | C23×C3 | — | 36 | 2 | no | — |
| 230 | C23×C3 | — | 36 | 2 | no | — |
| 231 | C23×C3 | — | 72 | 2 | no | — |
| 232 | C23×C3 | — | 72 | 2 | no | — |
| 233 | C22×D3 | — | 12 | 1 | no | — |
| 234 | C22×D3 | — | 12 | 2 | no | — |
| 235 | C22×D3 | — | 12 | 1 | no | — |
| 236 | C22×D3 | — | 12 | 2 | no | — |
| 237 | C22×D3 | — | 24 | 2 | no | — |
| 238 | C22×D3 | — | 24 | 2 | no | — |
| 239 | C2×C3×C4 | — | 36 | 2 | no | — |
| 240 | C2×Dic3 | — | 12 | 2 | no | — |
| 241 | C2×Dic3 | — | 12 | 2 | no | — |
| 242 | C2×Dic3 | — | 24 | 2 | no | — |
| 243 | C2×Dic3 | — | 36 | 2 | no | — |
| 244 | C2×Dic3 | — | 72 | 2 | no | — |
| 245 | C2×Dic3 | — | 72 | 2 | no | — |
| 246 | C4×D3 | — | 72 | 2 | no | — |
| 247 | C4×D3 | — | 72 | 2 | no | — |
| 248 | SL(2,𝔽3) | — | 9 | 1 | no | — |
| 249 | C2×C32 | — | 2 | 2 | no | — |
| 250 | C2×C32 | — | 4 | 2 | no | — |
| 251 | C2×C32 | — | 4 | 1 | no | — |
| 252 | C2×C32 | — | 8 | 2 | no | — |
| 253 | C2×C32 | — | 8 | 1 | no | — |
| 254 | C2×C32 | — | 8 | 2 | no | — |
| 255 | C2×C32 | — | 16 | 2 | no | — |
| 256 | C2×C32 | C2×#859 | 1 | 1 | yes | characteristic |
| 257 | C2×C32 | #5421 | 1 | 2 | yes | — |
| 258 | C3⋊D3 | — | 2 | 2 | no | — |
| 259 | C3⋊D3 | #5419 | 1 | 2 | yes | — |
| 260 | C3⋊D3 | #5420 | 1 | 1 | yes | characteristic |
| 261 | C3⋊D3 | #5432 | 1 | 1 | yes | characteristic |
| 262 | C3×D3 | — | 12 | 2 | no | — |
| 263 | C3×D3 | — | 12 | 1 | no | — |
| 264 | C3×D3 | — | 12 | 1 | no | — |
| 265 | C3×D3 | — | 24 | 2 | no | — |
| 266 | C24 | — | 9 | 1 | no | — |
| 267 | C2×Q8 | — | 9 | 1 | no | — |
| 268 | C2×Q8 | — | 9 | 2 | no | — |
| 269 | C2×Q8 | — | 18 | 2 | no | — |
| 270 | C2×Q8 | — | 27 | 2 | no | — |
| 271 | C2×Q8 | — | 27 | 1 | no | — |
| 272 | C2×Q8 | — | 27 | 2 | no | — |
| 273 | C2×Q8 | — | 27 | 4 | no | — |
| 274 | C2×Q8 | — | 54 | 1 | no | — |
| 275 | C2×Q8 | — | 54 | 2 | no | — |
| 276 | C2×Q8 | — | 54 | 4 | no | — |
| 277 | C2×Q8 | — | 54 | 2 | no | — |
| 278 | C2×Q8 | — | 54 | 4 | no | — |
| 279 | C22×C4 | — | 27 | 1 | no | — |
| 280 | C22×C4 | — | 27 | 1 | no | — |
| 281 | C22×C4 | — | 27 | 2 | no | — |
| 282 | C22×C4 | — | 27 | 2 | no | — |
| 283 | C22×C4 | — | 54 | 2 | no | — |
| 284 | C22×C4 | — | 54 | 2 | no | — |
| 285 | C22×C4 | — | 54 | 2 | no | — |
| 286 | C2×C8 | — | 54 | 2 | no | — |
| 287 | C2×C8 | — | 54 | 2 | no | — |
| 288 | C2×C8 | — | 54 | 2 | no | — |
| 289 | C4⋊C4 | — | 54 | 2 | no | — |
| 290 | C4⋊C4 | — | 54 | 2 | no | — |
| 291 | C22⋊C4 | — | 36 | 1 | no | — |
| 292 | C22⋊C4 | — | 108 | 1 | no | — |
| 293 | C22×C3 | — | 4 | 2 | no | — |
| 294 | C22×C3 | — | 4 | 1 | no | — |
| 295 | C22×C3 | — | 8 | 2 | no | — |
| 296 | C22×C3 | — | 12 | 2 | no | — |
| 297 | C22×C3 | — | 12 | 1 | no | — |
| 298 | C22×C3 | — | 24 | 2 | no | — |
| 299 | C22×C3 | — | 24 | 2 | no | — |
| 300 | C22×C3 | — | 24 | 1 | no | — |
| 301 | C22×C3 | — | 36 | 2 | no | — |
| 302 | C22×C3 | — | 36 | 2 | no | — |
| 303 | C22×C3 | — | 36 | 1 | no | — |
| 304 | C22×C3 | — | 36 | 1 | no | — |
| 305 | C22×C3 | — | 36 | 2 | no | — |
| 306 | C22×C3 | — | 48 | 2 | no | — |
| 307 | C22×C3 | — | 72 | 2 | no | — |
| 308 | C22×C3 | — | 72 | 2 | no | — |
| 309 | C22×C3 | — | 72 | 4 | no | — |
| 310 | C22×C3 | — | 72 | 2 | no | — |
| 311 | C2×D3 | — | 12 | 2 | no | — |
| 312 | C2×D3 | — | 12 | 2 | no | — |
| 313 | C2×D3 | — | 12 | 1 | no | — |
| 314 | C2×D3 | — | 12 | 1 | no | — |
| 315 | C2×D3 | — | 12 | 2 | no | — |
| 316 | C2×D3 | — | 24 | 2 | no | — |
| 317 | C2×D3 | — | 24 | 4 | no | — |
| 318 | C2×D3 | — | 24 | 2 | no | — |
| 319 | C2×D3 | — | 24 | 2 | no | — |
| 320 | C3×C4 | — | 72 | 2 | no | — |
| 321 | Dic3 | — | 24 | 2 | no | — |
| 322 | Dic3 | — | 24 | 2 | no | — |
| 323 | Dic3 | — | 48 | 2 | no | — |
| 324 | Dic3 | — | 72 | 2 | no | — |
| 325 | C32 | — | 4 | 1 | no | — |
| 326 | C32 | — | 8 | 1 | no | — |
| 327 | C32 | #73148 | 1 | 1 | yes | characteristic, complemented |
| 328 | C23 | — | 9 | 1 | no | — |
| 329 | C23 | — | 9 | 2 | no | — |
| 330 | C23 | — | 9 | 2 | no | — |
| 331 | C23 | — | 9 | 1 | no | — |
| 332 | C23 | — | 18 | 2 | no | — |
| 333 | C23 | — | 18 | 2 | no | — |
| 334 | C23 | AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 335 | Q8 | — | 9 | 1 | no | — |
| 336 | Q8 | — | 27 | 2 | no | — |
| 337 | Q8 | — | 27 | 1 | no | — |
| 338 | Q8 | — | 27 | 4 | no | — |
| 339 | Q8 | — | 54 | 1 | no | — |
| 340 | Q8 | — | 54 | 2 | no | — |
| 341 | Q8 | — | 54 | 4 | no | — |
| 342 | C2×C4 | — | 27 | 2 | no | — |
| 343 | C2×C4 | — | 27 | 2 | no | — |
| 344 | C2×C4 | — | 27 | 1 | no | — |
| 345 | C2×C4 | — | 27 | 1 | no | — |
| 346 | C2×C4 | — | 27 | 2 | no | — |
| 347 | C2×C4 | — | 36 | 2 | no | — |
| 348 | C2×C4 | — | 54 | 2 | no | — |
| 349 | C2×C4 | — | 54 | 4 | no | — |
| 350 | C2×C4 | — | 54 | 2 | no | — |
| 351 | C2×C4 | — | 54 | 2 | no | — |
| 352 | C2×C4 | — | 108 | 2 | no | — |
| 353 | C2×C4 | — | 108 | 2 | no | — |
| 354 | C8 | — | 108 | 2 | no | — |
| 355 | C2×C3 | — | 4 | 1 | no | — |
| 356 | C2×C3 | — | 4 | 2 | no | — |
| 357 | C2×C3 | — | 8 | 2 | no | — |
| 358 | C2×C3 | — | 12 | 1 | no | — |
| 359 | C2×C3 | — | 12 | 2 | no | — |
| 360 | C2×C3 | — | 24 | 2 | no | — |
| 361 | C2×C3 | — | 24 | 1 | no | — |
| 362 | C2×C3 | — | 24 | 2 | no | — |
| 363 | C2×C3 | — | 36 | 1 | no | — |
| 364 | C2×C3 | — | 36 | 2 | no | — |
| 365 | C2×C3 | — | 36 | 1 | no | — |
| 366 | C2×C3 | — | 48 | 2 | no | — |
| 367 | C2×C3 | — | 72 | 2 | no | — |
| 368 | D3 | — | 12 | 2 | no | — |
| 369 | D3 | — | 12 | 1 | no | — |
| 370 | D3 | — | 12 | 1 | no | — |
| 371 | D3 | — | 24 | 2 | no | — |
| 372 | C22 | — | 2 | 2 | no | — |
| 373 | C22 | — | 9 | 1 | no | — |
| 374 | C22 | — | 9 | 1 | no | — |
| 375 | C22 | — | 9 | 2 | no | — |
| 376 | C22 | — | 9 | 2 | no | — |
| 377 | C22 | — | 9 | 2 | no | — |
| 378 | C22 | — | 18 | 2 | no | — |
| 379 | C22 | — | 18 | 2 | no | — |
| 380 | C22 | — | 18 | 4 | no | — |
| 381 | C22 | — | 18 | 2 | no | — |
| 382 | C22 | (PSU(3,𝔽2)⋊C3)⋊C4 | 1 | 2 | yes | complemented |
| 383 | C22 | C2×AGL(2,𝔽3) | 1 | 1 | yes | characteristic |
| 384 | C4 | — | 27 | 2 | no | — |
| 385 | C4 | — | 27 | 1 | no | — |
| 386 | C4 | — | 27 | 1 | no | — |
| 387 | C4 | — | 54 | 2 | no | — |
| 388 | C4 | — | 72 | 2 | no | — |
| 389 | C3 | — | 4 | 1 | no | — |
| 390 | C3 | — | 12 | 1 | no | — |
| 391 | C3 | — | 24 | 1 | no | — |
| 392 | C2 | — | 2 | 2 | no | — |
| 393 | C2 | — | 9 | 1 | no | — |
| 394 | C2 | — | 9 | 1 | no | — |
| 395 | C2 | — | 9 | 2 | no | — |
| 396 | C2 | — | 18 | 2 | no | — |
| 397 | C2 | C2×(PSU(3,𝔽2)⋊C3)⋊C4 | 1 | 1 | yes | characteristic |
| 398 | C2 | #13180131 | 1 | 2 | yes | — |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×(PSU(3,𝔽2)⋊C3)⋊C4 | C2 | semidirect |
| 5. C22×PSU(3,𝔽2)⋊C3 | C4 | semidirect |
| 28. C22×PSU(3,𝔽2) | Dic3 | semidirect |
| 39. PSU(3,𝔽2)⋊C3 | C22⋊C4 | semidirect |
| 137. PSU(3,𝔽2) | #217 | semidirect |
| 180. C22×C32 | #859 | semidirect |
| 186. C2×C3⋊D3 | #859 | semidirect |
| 327. C32 | #73148 | semidirect |
| 382. C22 | (PSU(3,𝔽2)⋊C3)⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×PSU(3,𝔽2)⋊C3 | 2 |
| C2×(PSU(3,𝔽2)⋊C3)⋊C4 | 2 |
| #11784747 | 3 |
| #11721310 | 4 |
| #73148 | 9 |