Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
458 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 95 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. #79315 | C2 | semidirect |
| 5. #69813 | C2 | semidirect |
| 6. #67749 | C2 | semidirect |
| 7. #67662 | C2 | semidirect |
| 14. #5091 | C4 | semidirect |
| 15. #5091 | C4 | semidirect |
| 16. #5075 | C4 | semidirect |
| 17. #5075 | C4 | semidirect |
| 400. C3 | #9164 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83316 | 2 |
| #79315 | 2 |
| C3×#1530 | 2 |
| #71811 | 2 |
| #69813 | 2 |
| #67749 | 2 |
| #67662 | 2 |
| #9164 | 3 |