Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
396 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 99 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. C3×#2985 | C2 | semidirect |
| 3. #71822 | C2 | semidirect |
| 6. #67756 | C2 | semidirect |
| 7. #67740 | C2 | semidirect |
| 31. #2985 | D3 | semidirect |
| 319. C3 | #9284 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2985 | 2 |
| #83359 | 2 |
| #71822 | 2 |
| #70806 | 2 |
| #70765 | 2 |
| #67756 | 2 |
| #67740 | 2 |
| #9284 | 3 |