Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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. #74222 | C2 | semidirect |
| 5. #67738 | C2 | semidirect |
| 6. #67736 | C2 | semidirect |
| 7. #67631 | C2 | semidirect |
| 326. C3 | #10366 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #74222 | 2 |
| C3×#1517 | 2 |
| #71815 | 2 |
| #71814 | 2 |
| #67738 | 2 |
| #67736 | 2 |
| #67631 | 2 |
| #10366 | 3 |