Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
414 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 414 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 |
|---|---|---|
| 4. #70771 | C2 | semidirect |
| 5. #70515 | C2 | semidirect |
| 6. C3×#1299 | C2 | semidirect |
| 7. #67665 | C2 | semidirect |
| 24. #4715 | C4 | semidirect |
| 25. #4714 | C4 | semidirect |
| 26. #4703 | C4 | semidirect |
| 27. #4702 | C4 | semidirect |
| 42. #1299 | D3 | semidirect |
| 391. C3 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79054 | 2 |
| #78539 | 2 |
| #70788 | 2 |
| #70771 | 2 |
| #70515 | 2 |
| C3×#1299 | 2 |
| #67665 | 2 |
| #8998 | 3 |