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 |
|---|---|---|
| 3. C3×#1531 | C2 | semidirect |
| 4. #71838 | C2 | semidirect |
| 6. #67751 | C2 | semidirect |
| 7. #67659 | C2 | semidirect |
| 15. #5089 | C4 | semidirect |
| 16. #5086 | C4 | semidirect |
| 17. #5082 | C4 | semidirect |
| 18. #5081 | C4 | semidirect |
| 38. #1531 | D3 | semidirect |
| 390. C3 | #9431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83346 | 2 |
| #78481 | 2 |
| C3×#1531 | 2 |
| #71838 | 2 |
| #70834 | 2 |
| #67751 | 2 |
| #67659 | 2 |
| #9431 | 3 |