Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 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. #83894 | C2 | semidirect |
| 2. #78499 | C2 | semidirect |
| 3. C3×#1975 | C2 | semidirect |
| 4. #70690 | C2 | semidirect |
| 5. #67663 | C2 | semidirect |
| 27. #1975 | D3 | semidirect |
| 33. C2×C3×Q16 | D4 | semidirect |
| 35. C2×C3×D8 | D4 | semidirect |
| 67. C2×C3⋊C16 | D4 | semidirect |
| 143. C2×Q16 | D12 | semidirect |
| 149. C2×D8 | D12 | semidirect |
| 320. C3 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83894 | 2 |
| #78499 | 2 |
| C3×#1975 | 2 |
| #70690 | 2 |
| #67663 | 2 |
| #13340 | 3 |