Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
652 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 103 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. #83370 | C2 | semidirect |
| 4. C3×#1994 | C2 | semidirect |
| 5. #70507 | C2 | semidirect |
| 7. #67611 | C2 | semidirect |
| 33. #1994 | D3 | semidirect |
| 351. C3 | #10291 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #83370 | 2 |
| #83355 | 2 |
| #73313 | 2 |
| C3×#1994 | 2 |
| #70507 | 2 |
| #70502 | 2 |
| #67611 | 2 |
| #10291 | 3 |