Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
574 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 574 conjugacy classes of subgroups — too many to draw. Only its 101 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×#3226 | C2 | semidirect |
| 3. #83215 | C2 | semidirect |
| 4. #71814 | C2 | semidirect |
| 5. #71786 | C2 | semidirect |
| 6. #70790 | C2 | semidirect |
| 7. #67741 | C2 | semidirect |
| 33. #3226 | D3 | semidirect |
| 387. C3 | #10225 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3226 | 2 |
| #83286 | 2 |
| #83215 | 2 |
| #71814 | 2 |
| #71786 | 2 |
| #70790 | 2 |
| #67741 | 2 |
| #10225 | 3 |