Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
554 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 109 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. #79264 | C2 | semidirect |
| 4. #70528 | C2 | semidirect |
| 6. C3×#1303 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 33. #1303 | D3 | semidirect |
| 356. C3 | #9406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79264 | 2 |
| #73712 | 2 |
| #70774 | 2 |
| #70528 | 2 |
| #70502 | 2 |
| C3×#1303 | 2 |
| #67620 | 2 |
| #9406 | 3 |