Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
368 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 71 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 |
|---|---|---|
| 2. #70916 | C2 | semidirect |
| 3. #69066 | C2 | semidirect |
| 5. C3×#1332 | C2 | semidirect |
| 7. #67474 | C2 | semidirect |
| 31. #1332 | D3 | semidirect |
| 162. D12 | Q32 | semidirect |
| 272. C3 | #12322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q16×D12 | 2 |
| #70916 | 2 |
| #69066 | 2 |
| #68577 | 2 |
| C3×#1332 | 2 |
| #67503 | 2 |
| #67474 | 2 |
| #12322 | 3 |