Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
452 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 89 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. #79054 | C2 | semidirect |
| 3. #70788 | C2 | semidirect |
| 4. #70765 | C2 | semidirect |
| 5. #70513 | C2 | semidirect |
| 6. C3×#1299 | C2 | semidirect |
| 7. #67665 | C2 | semidirect |
| 26. #4714 | C4 | semidirect |
| 27. #4713 | C4 | semidirect |
| 28. #4712 | C4 | semidirect |
| 29. #4702 | C4 | semidirect |
| 42. #1299 | D3 | semidirect |
| 424. C3 | #8997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79054 | 2 |
| #78532 | 2 |
| #70788 | 2 |
| #70765 | 2 |
| #70513 | 2 |
| C3×#1299 | 2 |
| #67665 | 2 |
| #8997 | 3 |