Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
294 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 109 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 |
|---|---|---|
| 21. #4480 | C4 | semidirect |
| 23. #4479 | C4 | semidirect |
| 241. C3 | #9632 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1570 | 2 |
| #70745 | 2 |
| #70516 | 2 |
| #70466 | 2 |
| #70422 | 2 |
| #67746 | 2 |
| #67715 | 2 |
| #9632 | 3 |