Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
436 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 436 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. #79279 | C2 | semidirect |
| 3. #70834 | C2 | semidirect |
| 4. #70806 | C2 | semidirect |
| 5. #70790 | C2 | semidirect |
| 6. C3×#1302 | C2 | semidirect |
| 7. #67659 | C2 | semidirect |
| 22. #4714 | C4 | semidirect |
| 23. #4713 | C4 | semidirect |
| 24. #4712 | C4 | semidirect |
| 27. #4702 | C4 | semidirect |
| 41. #1302 | D3 | semidirect |
| 409. C3 | #9432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #79279 | 2 |
| #78500 | 2 |
| #70834 | 2 |
| #70806 | 2 |
| #70790 | 2 |
| C3×#1302 | 2 |
| #67659 | 2 |
| #9432 | 3 |