Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 89 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. #74222 | C2 | semidirect |
| 5. C3×#1286 | C2 | semidirect |
| 6. #67736 | C2 | semidirect |
| 7. #67713 | C2 | semidirect |
| 29. #1286 | D3 | semidirect |
| 326. C3 | #10368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #74222 | 2 |
| #70790 | 2 |
| #70512 | 2 |
| #69545 | 2 |
| C3×#1286 | 2 |
| #67736 | 2 |
| #67713 | 2 |
| #10368 | 3 |