Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #79317 | C2 | semidirect |
| 5. #70837 | C2 | semidirect |
| 6. #67753 | C2 | semidirect |
| 7. #67752 | C2 | semidirect |
| 13. #5093 | C4 | semidirect |
| 14. #5078 | C4 | semidirect |
| 15. #5076 | C4 | semidirect |
| 16. #5070 | C4 | semidirect |
| 305. C3 | #9418 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83294 | 2 |
| #79317 | 2 |
| C3×#1536 | 2 |
| #71813 | 2 |
| #70837 | 2 |
| #67753 | 2 |
| #67752 | 2 |
| #9418 | 3 |