Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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. #79286 | C2 | semidirect |
| 3. #70774 | C2 | semidirect |
| 4. #70527 | C2 | semidirect |
| 5. #70502 | C2 | semidirect |
| 6. C3×#1303 | C2 | semidirect |
| 7. #67620 | C2 | semidirect |
| 33. #1303 | D3 | semidirect |
| 62. C3×C4⋊C8 | D4 | semidirect |
| 71. C4⋊(C3⋊C8) | D4 | semidirect |
| 174. C4⋊C8 | D12 | semidirect |
| 385. C3 | #9397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79286 | 2 |
| #73799 | 2 |
| #70774 | 2 |
| #70527 | 2 |
| #70502 | 2 |
| C3×#1303 | 2 |
| #67620 | 2 |
| #9397 | 3 |