Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
312 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 312 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. C3×#1450 | C2 | semidirect |
| 4. #70748 | C2 | semidirect |
| 6. #67743 | C2 | semidirect |
| 7. #67656 | C2 | semidirect |
| 32. #1450 | D3 | semidirect |
| 291. C3 | #9586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1450 | 2 |
| #70773 | 2 |
| #70761 | 2 |
| #70748 | 2 |
| #69735 | 2 |
| #67743 | 2 |
| #67656 | 2 |
| #9586 | 3 |