Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
296 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 87 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×#1713 | C2 | semidirect |
| 3. #71310 | C2 | semidirect |
| 5. #67438 | C2 | semidirect |
| 20. #1713 | D3 | semidirect |
| 97. C3×C8 | SD32 | semidirect |
| 139. C8 | #828 | semidirect |
| 154. C3 | #12526 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#1713 | 2 |
| #71313 | 2 |
| #71310 | 2 |
| #68058 | 2 |
| #67438 | 2 |
| #12526 | 3 |