Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
572 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 572 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×D16 | C2 | semidirect |
| 2. C2×#5160 | C2 | semidirect |
| 3. #83836 | C2 | semidirect |
| 4. C2×#4563 | C2 | semidirect |
| 5. #72033 | C2 | semidirect |
| 6. C2×#4508 | C2 | semidirect |
| 7. #67807 | C2 | semidirect |
| 30. C22×D16 | D3 | semidirect |
| 51. C2×C3×D8 | D4 | semidirect |
| 73. C2×C3×C16 | D4 | semidirect |
| 77. #819 | D4 | semidirect |
| 178. C2×D8 | #67 | semidirect |
| 199. C2×C16 | #67 | semidirect |
| 391. C3 | #13319 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×D16 | 2 |
| C2×#5160 | 2 |
| #83836 | 2 |
| C2×#4563 | 2 |
| #72033 | 2 |
| C2×#4508 | 2 |
| #67807 | 2 |
| #13319 | 3 |