Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×C3×#367 | C2 | semidirect |
| 3. C2×#4510 | C2 | semidirect |
| 4. C2×#4508 | C2 | semidirect |
| 5. #70646 | C2 | semidirect |
| 6. #70598 | C2 | semidirect |
| 7. #67723 | C2 | semidirect |
| 29. C2×#367 | D3 | semidirect |
| 62. C2×C3×C16 | D4 | semidirect |
| 176. C2×C16 | D12 | semidirect |
| 359. C3 | #13385 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79150 | 2 |
| C2×C3×#367 | 2 |
| C2×#4510 | 2 |
| C2×#4508 | 2 |
| #70646 | 2 |
| #70598 | 2 |
| #67723 | 2 |
| #13385 | 3 |