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. C22×#800 | C2 | semidirect |
| 2. C2×#4896 | C2 | semidirect |
| 4. C2×#4508 | C2 | semidirect |
| 5. C2×#4495 | C2 | semidirect |
| 6. #70654 | C2 | semidirect |
| 7. C3×#1382 | C2 | semidirect |
| 36. #1382 | D3 | semidirect |
| 52. C2×Dic12 | D4 | semidirect |
| 72. C2×C3×C16 | D4 | semidirect |
| 74. C3×#108 | D4 | semidirect |
| 199. C2×C16 | D12 | semidirect |
| 201. #108 | D12 | semidirect |
| 382. C3 | #13321 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#800 | 2 |
| C2×#4896 | 2 |
| #79183 | 2 |
| C2×#4508 | 2 |
| C2×#4495 | 2 |
| #70654 | 2 |
| C3×#1382 | 2 |
| #13321 | 3 |