Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. #79286 | C2 | semidirect |
| 3. #70762 | C2 | semidirect |
| 4. #70527 | C2 | semidirect |
| 5. #70496 | C2 | semidirect |
| 6. C3×#1286 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 34. #1286 | D3 | semidirect |
| 65. C3×C4×C8 | D4 | semidirect |
| 75. C4×C3⋊C8 | D4 | semidirect |
| 186. C4×C8 | D12 | semidirect |
| 411. C3 | #9485 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79286 | 2 |
| #74239 | 2 |
| #70762 | 2 |
| #70527 | 2 |
| #70496 | 2 |
| C3×#1286 | 2 |
| #67631 | 2 |
| #9485 | 3 |