Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
520 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×C3×Q32 | C2 | semidirect |
| 4. C2×#4565 | C2 | semidirect |
| 5. #72061 | C2 | semidirect |
| 7. #67807 | C2 | semidirect |
| 30. C22×Q32 | D3 | semidirect |
| 371. C3 | #13322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×Q32 | 2 |
| C2×#5192 | 2 |
| #83887 | 2 |
| C2×#4565 | 2 |
| #72061 | 2 |
| C2×#4508 | 2 |
| #67807 | 2 |
| #13322 | 3 |