Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
414 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 414 conjugacy classes of subgroups — too many to draw. Only its 99 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. #70803 | C2 | semidirect |
| 5. #70515 | C2 | semidirect |
| 6. #67748 | C2 | semidirect |
| 7. #67710 | C2 | semidirect |
| 19. #5069 | C4 | semidirect |
| 20. #5064 | C4 | semidirect |
| 21. #5060 | C4 | semidirect |
| 22. #5055 | C4 | semidirect |
| 391. C3 | #8998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2995 | 2 |
| #83136 | 2 |
| #71754 | 2 |
| #70803 | 2 |
| #70515 | 2 |
| #67748 | 2 |
| #67710 | 2 |
| #8998 | 3 |