Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
650 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 650 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #73751 | C2 | semidirect |
| 3. #70832 | C2 | semidirect |
| 4. #70799 | C2 | semidirect |
| 5. #69492 | C2 | semidirect |
| 6. C3×#1285 | C2 | semidirect |
| 7. #67748 | C2 | semidirect |
| 20. #4843 | C4 | semidirect |
| 21. #4842 | C4 | semidirect |
| 36. #1285 | D3 | semidirect |
| 55. #874 | C2×C4 | semidirect |
| 62. #869 | C2×C4 | semidirect |
| 64. C3×C4⋊C8 | C2×C4 | semidirect |
| 177. C4⋊C8 | C4×D3 | semidirect |
| 228. D12 | #104 | semidirect |
| 385. C3 | #9325 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79343 | 2 |
| #73751 | 2 |
| #70832 | 2 |
| #70799 | 2 |
| #69492 | 2 |
| C3×#1285 | 2 |
| #67748 | 2 |
| #9325 | 3 |