Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1114 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 1114 conjugacy classes of subgroups — too many to draw. Only its 81 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 | Q8×C22⋊H(3,𝔽3) | C2 | 1 | 1 | yes | maximal, characteristic, complemented |
| 2 | C4⋊((C3⋊D3)⋊A4) | C2 | 1 | 3 | yes | maximal, complemented |
| 3 | C4×(C3⋊D3)⋊A4 | C2 | 1 | 3 | yes | maximal, complemented |
| 4 | C22×#3832 | C3 | 1 | 1 | yes | maximal, characteristic, complemented |
| 5 | A4×#239 | — | 3 | 1 | no | maximal |
| 6 | C2×(C3⋊D3)⋊A4 | C22 | 1 | 3 | yes | — |
| 7 | #88722 | — | 4 | 1 | no | maximal |
| 8 | C4×C22⋊H(3,𝔽3) | C22 | 1 | 3 | yes | — |
| 9 | (C3⋊Dic3)⋊A4 | C22 | 1 | 1 | yes | characteristic |
| 10 | C22×C32×Q8 | C2×C3 | 1 | 1 | yes | characteristic, complemented |
| 11 | C2×#3832 | — | 3 | 1 | no | — |
| 12 | C2×#3832 | — | 3 | 3 | no | — |
| 13 | C2×#3832 | — | 3 | 3 | no | — |
| 14 | C2×#3832 | — | 3 | 1 | no | — |
| 15 | C22×C4⋊(C3⋊D3) | C2×C3 | 1 | 3 | yes | complemented |
| 16 | C22×C4×C3⋊D3 | C2×C3 | 1 | 3 | yes | complemented |
| 17 | C3×Q8×A4 | — | 2 | 1 | no | — |
| 18 | C3×Q8×A4 | D3 | 1 | 1 | yes | characteristic, complemented |
| 19 | A4×D12 | — | 3 | 3 | no | — |
| 20 | C4×D3×A4 | — | 3 | 3 | no | — |
| 21 | C2×C22⋊H(3,𝔽3) | C23 | 1 | 1 | yes | characteristic |
| 22 | (C3⋊D3)⋊A4 | — | 2 | 3 | no | — |
| 23 | Q8×H(3,𝔽3) | — | 4 | 1 | no | — |
| 24 | C4⋊((C3⋊D3)⋊C3) | — | 4 | 3 | no | — |
| 25 | C4×(C3⋊D3)⋊C3 | — | 4 | 3 | no | — |
| 26 | C22×#239 | — | 3 | 1 | no | — |
| 27 | C22×#239 | — | 9 | 1 | no | — |
| 28 | A4×#41 | — | 9 | 1 | no | — |
| 29 | C23×C3⋊D3 | C22×C3 | 1 | 3 | yes | — |
| 30 | C2×D3×A4 | — | 3 | 3 | no | — |
| 31 | C2×C32×Q8 | — | 3 | 1 | no | — |
| 32 | C2×C32×Q8 | — | 3 | 3 | no | — |
| 33 | C22×C32×C4 | C22×C3 | 1 | 3 | yes | — |
| 34 | C22×C3⋊Dic3 | C22×C3 | 1 | 1 | yes | characteristic |
| 35 | #3832 | — | 3 | 6 | no | — |
| 36 | #3832 | — | 3 | 6 | no | — |
| 37 | #3832 | — | 3 | 2 | no | — |
| 38 | #3832 | — | 3 | 1 | no | — |
| 39 | #3832 | — | 3 | 3 | no | — |
| 40 | #3832 | — | 3 | 3 | no | — |
| 41 | #3832 | A4 | 1 | 1 | yes | characteristic, complemented |
| 42 | C2×C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 43 | C2×C4⋊(C3⋊D3) | — | 3 | 6 | no | — |
| 44 | C2×C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 45 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 46 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 47 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 48 | C2×C4×C3⋊D3 | — | 3 | 3 | no | — |
| 49 | C3×#239 | — | 12 | 1 | no | — |
| 50 | C3×C4×A4 | — | 2 | 3 | no | — |
| 51 | C3×C4×A4 | C2×D3 | 1 | 3 | yes | — |
| 52 | Dic3×A4 | — | 3 | 1 | no | — |
| 53 | C2×(C3⋊D3)⋊C3 | — | 4 | 3 | no | — |
| 54 | C22⋊H(3,𝔽3) | #41 | 1 | 1 | yes | characteristic, complemented |
| 55 | C4×H(3,𝔽3) | — | 4 | 3 | no | — |
| 56 | (C3⋊Dic3)⋊C3 | — | 4 | 1 | no | — |
| 57 | C22×C3×Q8 | — | 3 | 1 | no | — |
| 58 | C22×C3×Q8 | C3×D3 | 1 | 1 | yes | characteristic |
| 59 | C2×#239 | — | 9 | 1 | no | — |
| 60 | C2×#239 | — | 9 | 3 | no | — |
| 61 | C2×#239 | — | 9 | 9 | no | — |
| 62 | C2×#239 | — | 9 | 9 | no | — |
| 63 | C2×#239 | — | 9 | 3 | no | — |
| 64 | C2×#239 | — | 9 | 3 | no | — |
| 65 | C2×#239 | — | 9 | 3 | no | — |
| 66 | C2×#239 | — | 9 | 1 | no | — |
| 67 | C22×D12 | — | 3 | 3 | no | — |
| 68 | C22×D12 | — | 9 | 3 | no | — |
| 69 | C22×C4×D3 | — | 3 | 3 | no | — |
| 70 | C22×C4×D3 | — | 9 | 3 | no | — |
| 71 | Q8×A4 | — | 3 | 1 | no | — |
| 72 | Q8×A4 | — | 6 | 1 | no | — |
| 73 | D4×A4 | — | 9 | 3 | no | — |
| 74 | C2×C4×A4 | — | 9 | 3 | no | — |
| 75 | C23×C32 | C23×C3 | 1 | 1 | yes | characteristic |
| 76 | C22×C3⋊D3 | — | 2 | 3 | no | — |
| 77 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 78 | C22×C3⋊D3 | — | 3 | 3 | no | — |
| 79 | C22×C3⋊D3 | — | 6 | 3 | no | — |
| 80 | C2×C3×A4 | — | 2 | 1 | no | — |
| 81 | C2×C3×A4 | C22×D3 | 1 | 1 | yes | characteristic |
| 82 | D3×A4 | — | 6 | 3 | no | — |
| 83 | C32×Q8 | — | 3 | 2 | no | — |
| 84 | C32×Q8 | — | 3 | 3 | no | — |
| 85 | C32×Q8 | — | 4 | 1 | no | — |
| 86 | C32×Q8 | — | 8 | 1 | no | — |
| 87 | C32×Q8 | C2×A4 | 1 | 1 | yes | characteristic, complemented |
| 88 | C2×C32×C4 | — | 3 | 3 | no | — |
| 89 | C2×C32×C4 | — | 3 | 3 | no | — |
| 90 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 91 | C2×C3⋊Dic3 | — | 3 | 1 | no | — |
| 92 | C4⋊(C3⋊D3) | — | 3 | 6 | no | — |
| 93 | C4⋊(C3⋊D3) | — | 3 | 6 | no | — |
| 94 | C4⋊(C3⋊D3) | — | 3 | 3 | no | — |
| 95 | C4⋊(C3⋊D3) | C2×A4 | 1 | 3 | yes | complemented |
| 96 | C4×C3⋊D3 | — | 3 | 6 | no | — |
| 97 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 98 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 99 | C4×C3⋊D3 | — | 3 | 3 | no | — |
| 100 | C4×C3⋊D3 | C2×A4 | 1 | 3 | yes | complemented |
| 101 | C3×D12 | — | 12 | 3 | no | — |
| 102 | C3×C4×D3 | — | 12 | 3 | no | — |
| 103 | C22×#41 | — | 9 | 1 | no | Sylow |
| 104 | C2×H(3,𝔽3) | — | 4 | 1 | no | — |
| 105 | (C3⋊D3)⋊C3 | — | 8 | 3 | no | — |
| 106 | C23×D3 | — | 3 | 3 | no | — |
| 107 | C23×D3 | — | 9 | 3 | no | — |
| 108 | C22×A4 | — | 9 | 3 | no | — |
| 109 | C3×#41 | — | 36 | 1 | no | — |
| 110 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 111 | C2×C3×Q8 | — | 3 | 9 | no | — |
| 112 | C2×C3×Q8 | — | 3 | 3 | no | — |
| 113 | C2×C3×Q8 | — | 3 | 1 | no | — |
| 114 | C22×C3×C4 | — | 3 | 3 | no | — |
| 115 | C22×C3×C4 | C2×C3×D3 | 1 | 3 | yes | — |
| 116 | C22×Dic3 | — | 3 | 1 | no | — |
| 117 | C22×Dic3 | — | 9 | 1 | no | — |
| 118 | #239 | — | 3 | 1 | no | — |
| 119 | #239 | — | 9 | 1 | no | — |
| 120 | #239 | — | 9 | 3 | no | — |
| 121 | #239 | — | 9 | 3 | no | — |
| 122 | #239 | — | 9 | 9 | no | — |
| 123 | #239 | — | 9 | 9 | no | — |
| 124 | #239 | — | 9 | 2 | no | — |
| 125 | #239 | — | 9 | 6 | no | — |
| 126 | #239 | — | 9 | 6 | no | — |
| 127 | #239 | — | 9 | 18 | no | — |
| 128 | #239 | — | 9 | 18 | no | — |
| 129 | #239 | — | 9 | 6 | no | — |
| 130 | #239 | — | 9 | 3 | no | — |
| 131 | #239 | — | 9 | 1 | no | — |
| 132 | C2×D12 | — | 9 | 3 | no | — |
| 133 | C2×D12 | — | 9 | 9 | no | — |
| 134 | C2×D12 | — | 9 | 9 | no | — |
| 135 | C2×D12 | — | 9 | 18 | no | — |
| 136 | C2×D12 | — | 9 | 6 | no | — |
| 137 | C2×D12 | — | 9 | 3 | no | — |
| 138 | C2×C4×D3 | — | 9 | 3 | no | — |
| 139 | C2×C4×D3 | — | 9 | 9 | no | — |
| 140 | C2×C4×D3 | — | 9 | 9 | no | — |
| 141 | C2×C4×D3 | — | 9 | 9 | no | — |
| 142 | C2×C4×D3 | — | 9 | 9 | no | — |
| 143 | C2×C4×D3 | — | 9 | 3 | no | — |
| 144 | C2×C4×D3 | — | 9 | 3 | no | — |
| 145 | C2×C4×D3 | — | 9 | 3 | no | — |
| 146 | C4×A4 | — | 3 | 3 | no | — |
| 147 | C4×A4 | — | 6 | 3 | no | — |
| 148 | C4×A4 | — | 9 | 1 | no | — |
| 149 | C22×C32 | — | 3 | 1 | no | — |
| 150 | C22×C32 | — | 3 | 1 | no | — |
| 151 | C22×C32 | C3×#41 | 1 | 1 | yes | characteristic, complemented |
| 152 | C2×C3⋊D3 | — | 3 | 3 | no | — |
| 153 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 154 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 155 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 156 | C2×C3⋊D3 | — | 6 | 3 | no | — |
| 157 | C2×C3⋊D3 | C22×A4 | 1 | 3 | yes | — |
| 158 | C2×C3×D3 | — | 12 | 3 | no | — |
| 159 | C3×A4 | — | 2 | 1 | no | — |
| 160 | C3×A4 | #239 | 1 | 1 | yes | characteristic, complemented |
| 161 | C32×C4 | — | 3 | 3 | no | — |
| 162 | C32×C4 | — | 4 | 3 | no | — |
| 163 | C32×C4 | — | 8 | 3 | no | — |
| 164 | C32×C4 | C22×A4 | 1 | 3 | yes | — |
| 165 | C3⋊Dic3 | — | 3 | 1 | no | — |
| 166 | C3⋊Dic3 | C22×A4 | 1 | 1 | yes | characteristic |
| 167 | C3×Dic3 | — | 12 | 1 | no | — |
| 168 | C2×#41 | — | 27 | 1 | no | — |
| 169 | C2×#41 | — | 27 | 3 | no | — |
| 170 | C2×#41 | — | 27 | 3 | no | — |
| 171 | C2×#41 | — | 27 | 1 | no | — |
| 172 | C22×Q8 | (C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic, complemented |
| 173 | C22×D4 | — | 9 | 3 | no | — |
| 174 | C23×C4 | — | 9 | 3 | no | — |
| 175 | H(3,𝔽3) | — | 4 | 1 | no | Sylow |
| 176 | C23×C3 | — | 3 | 1 | no | — |
| 177 | C23×C3 | C22×C3×D3 | 1 | 1 | yes | characteristic |
| 178 | C22×D3 | — | 6 | 3 | no | — |
| 179 | C22×D3 | — | 9 | 3 | no | — |
| 180 | C22×D3 | — | 9 | 9 | no | — |
| 181 | C22×D3 | — | 9 | 9 | no | — |
| 182 | C22×D3 | — | 9 | 3 | no | — |
| 183 | C22×D3 | — | 18 | 3 | no | — |
| 184 | C22×D3 | — | 18 | 9 | no | — |
| 185 | C22×D3 | — | 18 | 3 | no | — |
| 186 | C2×A4 | — | 3 | 1 | no | — |
| 187 | C2×A4 | — | 6 | 1 | no | — |
| 188 | C2×A4 | — | 18 | 3 | no | — |
| 189 | C3×Q8 | — | 3 | 6 | no | — |
| 190 | C3×Q8 | — | 3 | 2 | no | — |
| 191 | C3×Q8 | — | 3 | 9 | no | — |
| 192 | C3×Q8 | — | 3 | 3 | no | — |
| 193 | C3×Q8 | — | 3 | 1 | no | — |
| 194 | C3×Q8 | — | 12 | 1 | no | — |
| 195 | C3×Q8 | — | 24 | 1 | no | — |
| 196 | C3×Q8 | D3×A4 | 1 | 1 | yes | characteristic |
| 197 | C3×D4 | — | 36 | 3 | no | — |
| 198 | C2×C3×C4 | — | 3 | 9 | no | — |
| 199 | C2×C3×C4 | — | 3 | 9 | no | — |
| 200 | C2×C3×C4 | — | 3 | 3 | no | — |
| 201 | C2×C3×C4 | — | 3 | 3 | no | — |
| 202 | C2×C3×C4 | — | 36 | 3 | no | — |
| 203 | C2×Dic3 | — | 9 | 1 | no | — |
| 204 | C2×Dic3 | — | 9 | 3 | no | — |
| 205 | C2×Dic3 | — | 9 | 3 | no | — |
| 206 | C2×Dic3 | — | 9 | 1 | no | — |
| 207 | D12 | — | 3 | 3 | no | — |
| 208 | D12 | — | 9 | 3 | no | — |
| 209 | D12 | — | 9 | 6 | no | — |
| 210 | D12 | — | 9 | 18 | no | — |
| 211 | D12 | — | 9 | 18 | no | — |
| 212 | D12 | — | 9 | 6 | no | — |
| 213 | D12 | — | 9 | 9 | no | — |
| 214 | D12 | — | 9 | 3 | no | — |
| 215 | C4×D3 | — | 3 | 3 | no | — |
| 216 | C4×D3 | — | 9 | 3 | no | — |
| 217 | C4×D3 | — | 9 | 3 | no | — |
| 218 | C4×D3 | — | 9 | 3 | no | — |
| 219 | C4×D3 | — | 9 | 9 | no | — |
| 220 | C4×D3 | — | 9 | 9 | no | — |
| 221 | C4×D3 | — | 9 | 18 | no | — |
| 222 | C4×D3 | — | 9 | 6 | no | — |
| 223 | C4×D3 | — | 9 | 9 | no | — |
| 224 | C4×D3 | — | 9 | 3 | no | — |
| 225 | C2×C32 | — | 3 | 1 | no | — |
| 226 | C2×C32 | — | 3 | 1 | no | — |
| 227 | C2×C32 | — | 4 | 1 | no | — |
| 228 | C2×C32 | — | 8 | 1 | no | — |
| 229 | C2×C32 | C23×A4 | 1 | 1 | yes | characteristic |
| 230 | C3⋊D3 | — | 2 | 3 | no | — |
| 231 | C3⋊D3 | — | 6 | 3 | no | — |
| 232 | C3×D3 | — | 24 | 3 | no | — |
| 233 | C24 | — | 9 | 3 | no | — |
| 234 | #41 | — | 9 | 1 | no | — |
| 235 | #41 | — | 27 | 3 | no | — |
| 236 | #41 | — | 27 | 3 | no | — |
| 237 | #41 | — | 27 | 2 | no | — |
| 238 | #41 | — | 27 | 6 | no | — |
| 239 | #41 | — | 27 | 6 | no | — |
| 240 | #41 | — | 27 | 1 | no | — |
| 241 | C2×Q8 | — | 3 | 3 | no | — |
| 242 | C2×Q8 | — | 3 | 1 | no | — |
| 243 | C2×D4 | — | 27 | 3 | no | — |
| 244 | C2×D4 | — | 27 | 3 | no | — |
| 245 | C2×D4 | — | 27 | 6 | no | — |
| 246 | C22×C4 | — | 9 | 1 | no | — |
| 247 | C22×C4 | — | 27 | 3 | no | — |
| 248 | C22×C4 | — | 27 | 3 | no | — |
| 249 | C22×C4 | — | 27 | 3 | no | — |
| 250 | C22×C4 | — | 27 | 3 | no | — |
| 251 | C22×C4 | C2×(C3⋊D3)⋊C3 | 1 | 3 | yes | — |
| 252 | C22×C3 | — | 3 | 1 | no | — |
| 253 | C22×C3 | — | 3 | 3 | no | — |
| 254 | C22×C3 | — | 3 | 3 | no | — |
| 255 | C22×C3 | — | 3 | 1 | no | — |
| 256 | C22×C3 | — | 3 | 1 | no | — |
| 257 | C22×C3 | — | 36 | 3 | no | — |
| 258 | C22×C3 | C3×#239 | 1 | 1 | yes | characteristic |
| 259 | C2×D3 | — | 3 | 3 | no | — |
| 260 | C2×D3 | — | 9 | 3 | no | — |
| 261 | C2×D3 | — | 9 | 9 | no | — |
| 262 | C2×D3 | — | 9 | 3 | no | — |
| 263 | C2×D3 | — | 18 | 3 | no | — |
| 264 | C2×D3 | — | 18 | 3 | no | — |
| 265 | C2×D3 | — | 18 | 9 | no | — |
| 266 | C2×D3 | — | 18 | 9 | no | — |
| 267 | C2×D3 | — | 18 | 9 | no | — |
| 268 | C2×D3 | — | 18 | 9 | no | — |
| 269 | C2×D3 | — | 18 | 3 | no | — |
| 270 | C2×D3 | — | 18 | 3 | no | — |
| 271 | A4 | — | 3 | 1 | no | — |
| 272 | A4 | — | 6 | 1 | no | — |
| 273 | C3×C4 | — | 3 | 9 | no | — |
| 274 | C3×C4 | — | 3 | 3 | no | — |
| 275 | C3×C4 | — | 3 | 3 | no | — |
| 276 | C3×C4 | — | 12 | 3 | no | — |
| 277 | C3×C4 | — | 24 | 3 | no | — |
| 278 | C3×C4 | — | 36 | 1 | no | — |
| 279 | C3×C4 | C2×D3×A4 | 1 | 3 | yes | — |
| 280 | Dic3 | — | 3 | 1 | no | — |
| 281 | Dic3 | — | 9 | 1 | no | — |
| 282 | Dic3 | — | 9 | 3 | no | — |
| 283 | Dic3 | — | 9 | 1 | no | — |
| 284 | C32 | — | 4 | 1 | no | — |
| 285 | C32 | — | 8 | 1 | no | — |
| 286 | C32 | A4×#41 | 1 | 1 | yes | characteristic, complemented |
| 287 | C23 | — | 18 | 3 | no | — |
| 288 | C23 | — | 27 | 3 | no | — |
| 289 | C23 | — | 27 | 3 | no | — |
| 290 | C23 | — | 54 | 3 | no | — |
| 291 | C23 | C22×(C3⋊D3)⋊C3 | 1 | 1 | yes | characteristic |
| 292 | Q8 | — | 3 | 2 | no | — |
| 293 | Q8 | — | 3 | 3 | no | — |
| 294 | Q8 | (C3⋊D3)⋊A4 | 1 | 1 | yes | characteristic, complemented |
| 295 | D4 | — | 9 | 3 | no | — |
| 296 | D4 | — | 27 | 6 | no | — |
| 297 | D4 | — | 27 | 6 | no | — |
| 298 | D4 | — | 27 | 3 | no | — |
| 299 | C2×C4 | — | 3 | 3 | no | — |
| 300 | C2×C4 | — | 3 | 3 | no | — |
| 301 | C2×C4 | — | 9 | 3 | no | — |
| 302 | C2×C4 | — | 27 | 3 | no | — |
| 303 | C2×C4 | — | 27 | 3 | no | — |
| 304 | C2×C4 | — | 27 | 6 | no | — |
| 305 | C2×C4 | — | 27 | 1 | no | — |
| 306 | C2×C4 | — | 27 | 3 | no | — |
| 307 | C2×C4 | — | 27 | 1 | no | — |
| 308 | C2×C3 | — | 3 | 3 | no | — |
| 309 | C2×C3 | — | 3 | 3 | no | — |
| 310 | C2×C3 | — | 3 | 1 | no | — |
| 311 | C2×C3 | — | 3 | 1 | no | — |
| 312 | C2×C3 | — | 3 | 1 | no | — |
| 313 | C2×C3 | — | 12 | 1 | no | — |
| 314 | C2×C3 | — | 24 | 1 | no | — |
| 315 | C2×C3 | — | 72 | 3 | no | — |
| 316 | C2×C3 | C22×D3×A4 | 1 | 1 | yes | characteristic |
| 317 | D3 | — | 6 | 3 | no | — |
| 318 | D3 | — | 18 | 3 | no | — |
| 319 | D3 | — | 18 | 9 | no | — |
| 320 | D3 | — | 18 | 3 | no | — |
| 321 | C22 | — | 3 | 1 | no | — |
| 322 | C22 | — | 3 | 1 | no | — |
| 323 | C22 | — | 9 | 3 | no | — |
| 324 | C22 | — | 27 | 3 | no | — |
| 325 | C22 | — | 54 | 3 | no | — |
| 326 | C22 | — | 54 | 3 | no | — |
| 327 | C22 | — | 54 | 3 | no | — |
| 328 | C22 | — | 54 | 3 | no | — |
| 329 | C22 | #88722 | 1 | 1 | yes | characteristic, complemented |
| 330 | C4 | — | 3 | 3 | no | — |
| 331 | C4 | — | 9 | 1 | no | — |
| 332 | C4 | — | 27 | 1 | no | — |
| 333 | C4 | C2×(C3⋊D3)⋊A4 | 1 | 3 | yes | — |
| 334 | C3 | — | 3 | 1 | no | — |
| 335 | C3 | — | 12 | 1 | no | — |
| 336 | C3 | — | 24 | 1 | no | — |
| 337 | C3 | A4×#239 | 1 | 1 | yes | characteristic |
| 338 | C2 | — | 3 | 1 | no | — |
| 339 | C2 | — | 3 | 1 | no | — |
| 340 | C2 | — | 18 | 3 | no | — |
| 341 | C2 | — | 54 | 3 | no | — |
| 342 | C2 | C22×(C3⋊D3)⋊A4 | 1 | 1 | yes | characteristic |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. Q8×C22⋊H(3,𝔽3) | C2 | semidirect |
| 2. C4⋊((C3⋊D3)⋊A4) | C2 | semidirect |
| 3. C4×(C3⋊D3)⋊A4 | C2 | semidirect |
| 4. C22×#3832 | C3 | semidirect |
| 10. C22×C32×Q8 | C2×C3 | semidirect |
| 15. C22×C4⋊(C3⋊D3) | C2×C3 | semidirect |
| 16. C22×C4×C3⋊D3 | C2×C3 | semidirect |
| 18. C3×Q8×A4 | D3 | semidirect |
| 41. #3832 | A4 | semidirect |
| 54. C22⋊H(3,𝔽3) | #41 | semidirect |
| 87. C32×Q8 | C2×A4 | semidirect |
| 95. C4⋊(C3⋊D3) | C2×A4 | semidirect |
| 100. C4×C3⋊D3 | C2×A4 | semidirect |
| 151. C22×C32 | C3×#41 | semidirect |
| 160. C3×A4 | #239 | semidirect |
| 172. C22×Q8 | (C3⋊D3)⋊C3 | semidirect |
| 286. C32 | A4×#41 | semidirect |
| 294. Q8 | (C3⋊D3)⋊A4 | semidirect |
| 329. C22 | #88722 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C22⋊H(3,𝔽3) | 2 |
| C4⋊((C3⋊D3)⋊A4) | 2 |
| C4×(C3⋊D3)⋊A4 | 2 |
| C22×#3832 | 3 |
| A4×#239 | 3 |
| #88722 | 4 |