Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
578 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 105 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. #79039 | C2 | semidirect |
| 3. #70782 | C2 | semidirect |
| 4. #70774 | C2 | semidirect |
| 5. #70502 | C2 | semidirect |
| 6. C3×#1286 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 36. #1286 | D3 | semidirect |
| 66. C3×C4⋊C8 | D4 | semidirect |
| 77. C4⋊(C3⋊C8) | D4 | semidirect |
| 189. C4⋊C8 | D12 | semidirect |
| 425. C3 | #9198 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79039 | 2 |
| #74244 | 2 |
| #70782 | 2 |
| #70774 | 2 |
| #70502 | 2 |
| C3×#1286 | 2 |
| #67631 | 2 |
| #9198 | 3 |