Finite Group DatabasebetaFinite Group DatabasebetaOrder 2916.
599 conjugacy classes of subgroups; only the 52 normal subgroups are shown.
This group has 599 conjugacy classes of subgroups — too many to draw. Only its 52 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 | C3⋊(#4184⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C3×#92283 | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 3 | C3⋊(#4177⋊C3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 4 | C3×#66432 | — | 3 | 1 | no | maximal |
| 5 | D3×C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | maximal |
| 6 | #11757738 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 7 | (#4176⋊C2)⋊C3 | — | 3 | 3 | no | maximal |
| 8 | C3×#6910 | C22 | 1 | 1 | yes | characteristic, complemented, Sylow |
| 9 | C3⋊(C3⋊AGL(1,ℤ/9)) | D3 | 1 | 1 | yes | characteristic, complemented |
| 10 | C3×C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 11 | C3×C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 12 | C32×#272 | D3 | 1 | 1 | yes | characteristic |
| 13 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 14 | C3×C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 15 | C3×D3×3−1+2 | — | 3 | 1 | no | — |
| 16 | C3⋊#4184 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 17 | #4184⋊C3 | — | 3 | 3 | no | — |
| 18 | #4184⋊C3 | — | 6 | 3 | no | — |
| 19 | C3⋊#4177 | — | 2 | 1 | no | — |
| 20 | C3⋊#4177 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 21 | #4177⋊C3 | — | 3 | 3 | no | — |
| 22 | #92283 | — | 2 | 3 | no | — |
| 23 | #92283 | D3 | 1 | 3 | yes | complemented |
| 24 | C3×#4176 | — | 2 | 1 | no | — |
| 25 | C3×#4176 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 26 | C3×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 27 | C3×D3×C3⋊D3 | — | 9 | 1 | no | — |
| 28 | C2×C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 29 | #66432 | — | 3 | 1 | no | — |
| 30 | D3×C3⋊D9 | — | 3 | 1 | no | — |
| 31 | D3×AGL(1,ℤ/9) | — | 9 | 3 | no | — |
| 32 | C3×((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 33 | #4176⋊C2 | — | 3 | 3 | no | — |
| 34 | C32×3−1+2 | — | 2 | 1 | no | — |
| 35 | C32×3−1+2 | C2×D3 | 1 | 1 | yes | characteristic, complemented |
| 36 | C32×H(3,𝔽3) | C2×D3 | 1 | 1 | yes | characteristic |
| 37 | #6910 | — | 2 | 3 | no | — |
| 38 | #6910 | — | 2 | 3 | no | — |
| 39 | #6910 | — | 4 | 3 | no | — |
| 40 | #6910 | C2×D3 | 1 | 3 | yes | complemented |
| 41 | C3×#731 | — | 2 | 1 | no | — |
| 42 | C3×#731 | — | 2 | 1 | no | — |
| 43 | C3×#731 | — | 4 | 1 | no | — |
| 44 | C3×#731 | C22×C3 | 1 | 1 | yes | characteristic, complemented |
| 45 | C3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 46 | C3×C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 47 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 48 | C32×C3⋊D3 | — | 9 | 1 | no | — |
| 49 | C33×D3 | — | 3 | 1 | no | — |
| 50 | C33×D3 | — | 9 | 1 | no | — |
| 51 | C2×C3×3−1+2 | — | 9 | 1 | no | — |
| 52 | C3⋊(C3⋊D9) | C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 53 | C3⋊AGL(1,ℤ/9) | — | 3 | 1 | no | — |
| 54 | C3⋊AGL(1,ℤ/9) | — | 3 | 3 | no | — |
| 55 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 56 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 57 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 58 | C3⋊AGL(1,ℤ/9) | — | 6 | 1 | no | — |
| 59 | C3⋊AGL(1,ℤ/9) | — | 9 | 1 | no | — |
| 60 | C3⋊AGL(1,ℤ/9) | — | 18 | 1 | no | — |
| 61 | C3×#272 | — | 2 | 1 | no | — |
| 62 | C3×#272 | C3×D3 | 1 | 1 | yes | characteristic |
| 63 | C3×#272 | C3⋊D3 | 1 | 1 | yes | characteristic |
| 64 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 65 | C3⋊((C3⋊D3)⋊C3) | — | 3 | 1 | no | — |
| 66 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 67 | C3⋊((C3⋊D3)⋊C3) | — | 6 | 1 | no | — |
| 68 | C3×C3⋊D9 | — | 3 | 1 | no | — |
| 69 | C3×C3⋊D9 | — | 6 | 1 | no | — |
| 70 | D3×3−1+2 | — | 3 | 3 | no | — |
| 71 | D3×3−1+2 | — | 6 | 3 | no | — |
| 72 | C3×AGL(1,ℤ/9) | — | 9 | 3 | no | — |
| 73 | C3×AGL(1,ℤ/9) | — | 18 | 3 | no | — |
| 74 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 75 | C3×(C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 76 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 77 | C3×(C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 78 | C3×D3×C9 | — | 3 | 1 | no | — |
| 79 | C3×D3×C9 | — | 6 | 1 | no | — |
| 80 | #4184 | — | 3 | 3 | no | — |
| 81 | #4184 | — | 6 | 3 | no | — |
| 82 | #4177 | — | 3 | 3 | no | — |
| 83 | #4177 | — | 6 | 3 | no | — |
| 84 | #4176 | — | 2 | 3 | no | — |
| 85 | #4176 | C3×D3 | 1 | 3 | yes | complemented |
| 86 | C2×C3×C3⋊D3 | — | 27 | 1 | no | — |
| 87 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 88 | D3×C3⋊D3 | — | 9 | 1 | no | — |
| 89 | C3×D32 | — | 27 | 1 | no | — |
| 90 | C3×D32 | — | 27 | 1 | no | — |
| 91 | C3×D32 | — | 27 | 3 | no | — |
| 92 | C3×D32 | — | 27 | 3 | no | — |
| 93 | C2×C3⋊D9 | — | 9 | 1 | no | — |
| 94 | C2×AGL(1,ℤ/9) | — | 27 | 3 | no | — |
| 95 | ((C3⋊D3)⋊C3)⋊C2 | — | 9 | 1 | no | — |
| 96 | D3×D9 | — | 9 | 3 | no | — |
| 97 | C34 | — | 3 | 1 | no | — |
| 98 | C34 | D32 | 1 | 1 | yes | characteristic |
| 99 | C3×3−1+2 | — | 2 | 3 | no | — |
| 100 | C3×3−1+2 | — | 2 | 1 | no | — |
| 101 | C3×3−1+2 | — | 2 | 3 | no | — |
| 102 | C3×3−1+2 | — | 3 | 1 | no | — |
| 103 | C3×3−1+2 | — | 4 | 3 | no | — |
| 104 | C3×3−1+2 | — | 4 | 1 | no | — |
| 105 | C3×3−1+2 | — | 6 | 1 | no | — |
| 106 | C3×3−1+2 | — | 6 | 1 | no | — |
| 107 | C3×3−1+2 | — | 6 | 1 | no | — |
| 108 | C3×3−1+2 | — | 6 | 1 | no | — |
| 109 | C3×3−1+2 | — | 12 | 1 | no | — |
| 110 | C3×3−1+2 | — | 12 | 1 | no | — |
| 111 | C3×3−1+2 | — | 12 | 1 | no | — |
| 112 | C3×3−1+2 | — | 12 | 1 | no | — |
| 113 | C3×3−1+2 | D32 | 1 | 3 | yes | complemented |
| 114 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 115 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 116 | C3×H(3,𝔽3) | — | 2 | 1 | no | — |
| 117 | C3×H(3,𝔽3) | — | 4 | 1 | no | — |
| 118 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 119 | C3×H(3,𝔽3) | — | 6 | 1 | no | — |
| 120 | C3×H(3,𝔽3) | — | 12 | 1 | no | — |
| 121 | C3×H(3,𝔽3) | C2×C3×D3 | 1 | 1 | yes | characteristic |
| 122 | C3×H(3,𝔽3) | C2×C3⋊D3 | 1 | 1 | yes | characteristic |
| 123 | C32×C9 | — | 2 | 1 | no | — |
| 124 | C32×C9 | — | 6 | 1 | no | — |
| 125 | C32×C9 | C2×C3×D3 | 1 | 1 | yes | characteristic, complemented |
| 126 | #731 | — | 2 | 3 | no | — |
| 127 | #731 | — | 2 | 3 | no | — |
| 128 | #731 | — | 2 | 3 | no | — |
| 129 | #731 | — | 4 | 3 | no | — |
| 130 | #731 | — | 4 | 3 | no | — |
| 131 | #731 | — | 4 | 6 | no | — |
| 132 | #731 | — | 4 | 3 | no | — |
| 133 | #731 | C2×C3×D3 | 1 | 3 | yes | complemented |
| 134 | C2×C33 | — | 9 | 1 | no | — |
| 135 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 136 | C3⋊(C3⋊D3) | — | 3 | 1 | no | — |
| 137 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 138 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 139 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 140 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 141 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 142 | C3×C3⋊D3 | — | 9 | 1 | no | — |
| 143 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 144 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 145 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 146 | C3×C3⋊D3 | — | 18 | 1 | no | — |
| 147 | C3×C3⋊D3 | — | 27 | 3 | no | — |
| 148 | C3×C3⋊D3 | — | 27 | 3 | no | — |
| 149 | C32×D3 | — | 3 | 1 | no | — |
| 150 | C32×D3 | — | 3 | 1 | no | — |
| 151 | C32×D3 | — | 6 | 1 | no | — |
| 152 | C32×D3 | — | 9 | 3 | no | — |
| 153 | C32×D3 | — | 9 | 1 | no | — |
| 154 | C32×D3 | — | 9 | 1 | no | — |
| 155 | C32×D3 | — | 9 | 3 | no | — |
| 156 | C32×D3 | — | 18 | 1 | no | — |
| 157 | C32×D3 | — | 18 | 3 | no | — |
| 158 | C32×D3 | — | 27 | 1 | no | — |
| 159 | C32×D3 | — | 27 | 3 | no | — |
| 160 | C32×D3 | — | 27 | 3 | no | — |
| 161 | C32×D3 | — | 27 | 1 | no | — |
| 162 | C2×3−1+2 | — | 9 | 3 | no | — |
| 163 | C2×3−1+2 | — | 18 | 3 | no | — |
| 164 | C2×C3×C9 | — | 9 | 1 | no | — |
| 165 | C2×C3×C9 | — | 18 | 1 | no | — |
| 166 | #272 | C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 167 | C3⋊D9 | — | 3 | 1 | no | — |
| 168 | C3⋊D9 | — | 3 | 3 | no | — |
| 169 | C3⋊D9 | — | 6 | 1 | no | — |
| 170 | C3⋊D9 | — | 9 | 1 | no | — |
| 171 | C3⋊D9 | — | 18 | 1 | no | — |
| 172 | AGL(1,ℤ/9) | — | 9 | 3 | no | — |
| 173 | AGL(1,ℤ/9) | — | 18 | 3 | no | — |
| 174 | AGL(1,ℤ/9) | — | 18 | 3 | no | — |
| 175 | AGL(1,ℤ/9) | — | 18 | 3 | no | — |
| 176 | AGL(1,ℤ/9) | — | 18 | 3 | no | — |
| 177 | AGL(1,ℤ/9) | — | 27 | 3 | no | — |
| 178 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 179 | (C3⋊D3)⋊C3 | — | 9 | 1 | no | — |
| 180 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 181 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 182 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 183 | (C3⋊D3)⋊C3 | — | 18 | 1 | no | — |
| 184 | (C3⋊D3)⋊C3 | — | 18 | 2 | no | — |
| 185 | (C3⋊D3)⋊C3 | — | 18 | 2 | no | — |
| 186 | D3×C9 | — | 3 | 3 | no | — |
| 187 | D3×C9 | — | 6 | 3 | no | — |
| 188 | C3×D9 | — | 9 | 3 | no | — |
| 189 | C3×D9 | — | 18 | 3 | no | — |
| 190 | C2×C3⋊D3 | — | 27 | 1 | no | — |
| 191 | C2×C3×D3 | — | 81 | 1 | no | — |
| 192 | C2×C3×D3 | — | 81 | 1 | no | — |
| 193 | C2×C3×D3 | — | 81 | 1 | no | — |
| 194 | C2×C3×D3 | — | 81 | 3 | no | — |
| 195 | D32 | — | 27 | 1 | no | — |
| 196 | D32 | — | 27 | 3 | no | — |
| 197 | D32 | — | 27 | 1 | no | — |
| 198 | D32 | — | 27 | 3 | no | — |
| 199 | C2×D9 | — | 27 | 3 | no | — |
| 200 | C33 | — | 2 | 1 | no | — |
| 201 | C33 | — | 2 | 1 | no | — |
| 202 | C33 | — | 2 | 1 | no | — |
| 203 | C33 | — | 3 | 1 | no | — |
| 204 | C33 | — | 3 | 1 | no | — |
| 205 | C33 | — | 4 | 1 | no | — |
| 206 | C33 | — | 6 | 1 | no | — |
| 207 | C33 | — | 6 | 1 | no | — |
| 208 | C33 | — | 6 | 1 | no | — |
| 209 | C33 | — | 9 | 3 | no | — |
| 210 | C33 | — | 9 | 3 | no | — |
| 211 | C33 | — | 12 | 1 | no | — |
| 212 | C33 | — | 18 | 3 | no | — |
| 213 | C33 | ((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 214 | C33 | C3×D32 | 1 | 1 | yes | characteristic |
| 215 | C33 | D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 216 | 3−1+2 | — | 2 | 3 | no | — |
| 217 | 3−1+2 | — | 3 | 3 | no | — |
| 218 | 3−1+2 | — | 4 | 3 | no | — |
| 219 | 3−1+2 | — | 6 | 3 | no | — |
| 220 | 3−1+2 | — | 6 | 3 | no | — |
| 221 | 3−1+2 | — | 6 | 3 | no | — |
| 222 | 3−1+2 | — | 6 | 3 | no | — |
| 223 | 3−1+2 | — | 12 | 3 | no | — |
| 224 | 3−1+2 | — | 12 | 1 | no | — |
| 225 | 3−1+2 | — | 12 | 3 | no | — |
| 226 | 3−1+2 | — | 12 | 3 | no | — |
| 227 | 3−1+2 | — | 12 | 2 | no | — |
| 228 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 229 | H(3,𝔽3) | — | 2 | 1 | no | — |
| 230 | H(3,𝔽3) | — | 4 | 1 | no | — |
| 231 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 232 | H(3,𝔽3) | — | 6 | 1 | no | — |
| 233 | H(3,𝔽3) | — | 6 | 2 | no | — |
| 234 | H(3,𝔽3) | — | 6 | 2 | no | — |
| 235 | H(3,𝔽3) | — | 12 | 1 | no | — |
| 236 | H(3,𝔽3) | — | 12 | 2 | no | — |
| 237 | H(3,𝔽3) | C2×C3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 238 | C3×C9 | — | 2 | 3 | no | — |
| 239 | C3×C9 | — | 3 | 1 | no | — |
| 240 | C3×C9 | — | 6 | 1 | no | — |
| 241 | C3×C9 | — | 6 | 1 | no | — |
| 242 | C3×C9 | — | 6 | 1 | no | — |
| 243 | C3×C9 | — | 6 | 3 | no | — |
| 244 | C3×C9 | — | 12 | 1 | no | — |
| 245 | C3×C9 | — | 12 | 3 | no | — |
| 246 | C3×C9 | — | 12 | 1 | no | — |
| 247 | C3×C9 | C3×D32 | 1 | 3 | yes | complemented |
| 248 | C2×C32 | — | 9 | 1 | no | — |
| 249 | C2×C32 | — | 9 | 1 | no | — |
| 250 | C2×C32 | — | 18 | 1 | no | — |
| 251 | C2×C32 | — | 27 | 3 | no | — |
| 252 | C2×C32 | — | 81 | 1 | no | — |
| 253 | C2×C32 | — | 81 | 1 | no | — |
| 254 | C3⋊D3 | — | 9 | 1 | no | — |
| 255 | C3⋊D3 | — | 9 | 1 | no | — |
| 256 | C3⋊D3 | — | 9 | 1 | no | — |
| 257 | C3⋊D3 | — | 9 | 1 | no | — |
| 258 | C3⋊D3 | — | 18 | 1 | no | — |
| 259 | C3⋊D3 | — | 18 | 1 | no | — |
| 260 | C3⋊D3 | — | 27 | 3 | no | — |
| 261 | C3⋊D3 | — | 27 | 3 | no | — |
| 262 | C3×D3 | — | 3 | 3 | no | — |
| 263 | C3×D3 | — | 3 | 1 | no | — |
| 264 | C3×D3 | — | 9 | 1 | no | — |
| 265 | C3×D3 | — | 9 | 1 | no | — |
| 266 | C3×D3 | — | 9 | 3 | no | — |
| 267 | C3×D3 | — | 9 | 1 | no | — |
| 268 | C3×D3 | — | 18 | 1 | no | — |
| 269 | C3×D3 | — | 18 | 1 | no | — |
| 270 | C3×D3 | — | 18 | 3 | no | — |
| 271 | C3×D3 | — | 27 | 1 | no | — |
| 272 | C3×D3 | — | 27 | 3 | no | — |
| 273 | C3×D3 | — | 27 | 3 | no | — |
| 274 | C3×D3 | — | 27 | 3 | no | — |
| 275 | C3×D3 | — | 27 | 3 | no | — |
| 276 | C3×D3 | — | 27 | 1 | no | — |
| 277 | C3×D3 | — | 27 | 1 | no | — |
| 278 | C3×D3 | — | 27 | 1 | no | — |
| 279 | C3×D3 | — | 54 | 1 | no | — |
| 280 | C3×D3 | — | 54 | 1 | no | — |
| 281 | C3×D3 | — | 54 | 3 | no | — |
| 282 | C3×D3 | — | 54 | 3 | no | — |
| 283 | C3×D3 | — | 81 | 1 | no | — |
| 284 | C3×D3 | — | 81 | 1 | no | — |
| 285 | C3×D3 | — | 162 | 1 | no | — |
| 286 | C3×D3 | — | 162 | 1 | no | — |
| 287 | C2×C9 | — | 9 | 3 | no | — |
| 288 | C2×C9 | — | 18 | 3 | no | — |
| 289 | D9 | — | 9 | 3 | no | — |
| 290 | D9 | — | 18 | 3 | no | — |
| 291 | D9 | — | 27 | 3 | no | — |
| 292 | C22×C3 | — | 243 | 1 | no | — |
| 293 | C2×D3 | — | 81 | 1 | no | — |
| 294 | C2×D3 | — | 81 | 1 | no | — |
| 295 | C2×D3 | — | 81 | 1 | no | — |
| 296 | C2×D3 | — | 81 | 3 | no | — |
| 297 | C32 | — | 2 | 1 | no | — |
| 298 | C32 | — | 2 | 1 | no | — |
| 299 | C32 | — | 2 | 1 | no | — |
| 300 | C32 | — | 3 | 3 | no | — |
| 301 | C32 | — | 3 | 3 | no | — |
| 302 | C32 | — | 3 | 1 | no | — |
| 303 | C32 | — | 4 | 1 | no | — |
| 304 | C32 | — | 6 | 3 | no | — |
| 305 | C32 | — | 6 | 1 | no | — |
| 306 | C32 | — | 6 | 1 | no | — |
| 307 | C32 | — | 9 | 1 | no | — |
| 308 | C32 | — | 9 | 1 | no | — |
| 309 | C32 | — | 9 | 3 | no | — |
| 310 | C32 | — | 12 | 1 | no | — |
| 311 | C32 | — | 18 | 1 | no | — |
| 312 | C32 | — | 18 | 1 | no | — |
| 313 | C32 | — | 18 | 1 | no | — |
| 314 | C32 | — | 18 | 1 | no | — |
| 315 | C32 | — | 18 | 3 | no | — |
| 316 | C32 | — | 18 | 3 | no | — |
| 317 | C32 | — | 36 | 1 | no | — |
| 318 | C32 | — | 36 | 1 | no | — |
| 319 | C32 | — | 36 | 3 | no | — |
| 320 | C32 | C3×((C3⋊D3)⋊C3)⋊C2 | 1 | 1 | yes | characteristic |
| 321 | C32 | ((C3⋊D3)⋊C3)⋊D3 | 1 | 1 | yes | characteristic |
| 322 | C32 | C3×D3×C3⋊D3 | 1 | 1 | yes | characteristic |
| 323 | C9 | — | 3 | 3 | no | — |
| 324 | C9 | — | 6 | 3 | no | — |
| 325 | C9 | — | 6 | 3 | no | — |
| 326 | C9 | — | 12 | 3 | no | — |
| 327 | C2×C3 | — | 9 | 3 | no | — |
| 328 | C2×C3 | — | 9 | 1 | no | — |
| 329 | C2×C3 | — | 27 | 1 | no | — |
| 330 | C2×C3 | — | 54 | 1 | no | — |
| 331 | C2×C3 | — | 81 | 1 | no | — |
| 332 | C2×C3 | — | 81 | 1 | no | — |
| 333 | C2×C3 | — | 81 | 1 | no | — |
| 334 | C2×C3 | — | 81 | 1 | no | — |
| 335 | C2×C3 | — | 162 | 1 | no | — |
| 336 | C2×C3 | — | 162 | 1 | no | — |
| 337 | D3 | — | 3 | 1 | no | — |
| 338 | D3 | — | 9 | 1 | no | — |
| 339 | D3 | — | 27 | 3 | no | — |
| 340 | D3 | — | 27 | 3 | no | — |
| 341 | D3 | — | 27 | 1 | no | — |
| 342 | D3 | — | 27 | 1 | no | — |
| 343 | D3 | — | 81 | 1 | no | — |
| 344 | D3 | — | 81 | 1 | no | — |
| 345 | D3 | — | 162 | 1 | no | — |
| 346 | D3 | — | 162 | 1 | no | — |
| 347 | C22 | — | 243 | 1 | no | Sylow |
| 348 | C3 | — | 3 | 1 | no | — |
| 349 | C3 | — | 3 | 1 | no | — |
| 350 | C3 | — | 6 | 1 | no | — |
| 351 | C3 | — | 6 | 1 | no | — |
| 352 | C3 | — | 6 | 1 | no | — |
| 353 | C3 | — | 9 | 1 | no | — |
| 354 | C3 | — | 12 | 1 | no | — |
| 355 | C3 | — | 18 | 1 | no | — |
| 356 | C3 | — | 18 | 1 | no | — |
| 357 | C3 | — | 36 | 1 | no | — |
| 358 | C3 | (#4176⋊C2)⋊C3 | 1 | 3 | yes | complemented |
| 359 | C3 | C3×((C3⋊D3)⋊C3)⋊D3 | 1 | 1 | yes | characteristic |
| 360 | C2 | — | 9 | 1 | no | — |
| 361 | C2 | — | 81 | 1 | no | — |
| 362 | C2 | — | 81 | 1 | no | — |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, cosocle, hypocenter | C3×#731 | C22×C3 |
| Frattini | C32 | C3×D3×C3⋊D3 |
| Fitting | C3×#6910 | C22 |
| socle | C32 | C3×((C3⋊D3)⋊C3)⋊C2 |
| LCS | G ▷ C3×#731 | |
| UCS | C1 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3⋊(#4184⋊C3) | C2 | semidirect |
| 2. C3×#92283 | C2 | semidirect |
| 3. C3⋊(#4177⋊C3) | C2 | semidirect |
| 6. #11757738 | C3 | semidirect |
| 8. C3×#6910 | C22 | semidirect |
| 9. C3⋊(C3⋊AGL(1,ℤ/9)) | D3 | semidirect |
| 16. C3⋊#4184 | C2×C3 | semidirect |
| 20. C3⋊#4177 | C2×C3 | semidirect |
| 23. #92283 | D3 | semidirect |
| 25. C3×#4176 | C2×C3 | semidirect |
| 35. C32×3−1+2 | C2×D3 | semidirect |
| 40. #6910 | C2×D3 | semidirect |
| 44. C3×#731 | C22×C3 | semidirect |
| 52. C3⋊(C3⋊D9) | C3×D3 | semidirect |
| 85. #4176 | C3×D3 | semidirect |
| 113. C3×3−1+2 | D32 | semidirect |
| 125. C32×C9 | C2×C3×D3 | semidirect |
| 133. #731 | C2×C3×D3 | semidirect |
| 247. C3×C9 | C3×D32 | semidirect |
| 358. C3 | (#4176⋊C2)⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊(#4184⋊C3) | 2 |
| C3×#92283 | 2 |
| C3⋊(#4177⋊C3) | 2 |
| C3×#66432 | 3 |
| D3×C3⋊AGL(1,ℤ/9) | 3 |
| #11757738 | 3 |
| (#4176⋊C2)⋊C3 | 3 |