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. #73412 | C2 | semidirect |
| 3. #69867 | C2 | semidirect |
| 4. #69855 | C2 | semidirect |
| 5. #69432 | C2 | semidirect |
| 6. C3×#1300 | C2 | semidirect |
| 7. #67750 | C2 | semidirect |
| 19. #4843 | C4 | semidirect |
| 20. #4842 | C4 | semidirect |
| 35. #1300 | D3 | semidirect |
| 54. #874 | C2×C4 | semidirect |
| 62. #869 | C2×C4 | semidirect |
| 63. 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 |
| #73412 | 2 |
| #69867 | 2 |
| #69855 | 2 |
| #69432 | 2 |
| C3×#1300 | 2 |
| #67750 | 2 |
| #9325 | 3 |