Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
316 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 316 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×#2247 | C2 | semidirect |
| 3. #71312 | C2 | semidirect |
| 4. #71298 | C2 | semidirect |
| 7. #67498 | C2 | semidirect |
| 25. #2247 | D3 | semidirect |
| 187. C3 | #12520 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#2247 | 2 |
| #71313 | 2 |
| #71312 | 2 |
| #71298 | 2 |
| #71297 | 2 |
| #69061 | 2 |
| #67498 | 2 |
| #12520 | 3 |