Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
364 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 97 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×#3162 | C2 | semidirect |
| 4. #67727 | C2 | semidirect |
| 5. #67663 | C2 | semidirect |
| 18. #3162 | D3 | semidirect |
| 33. C2×Dic12 | Q8 | semidirect |
| 36. C2×D24 | Q8 | semidirect |
| 231. C3 | #13373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3162 | 2 |
| #70656 | 2 |
| #69845 | 2 |
| #67727 | 2 |
| #67663 | 2 |
| #13373 | 3 |