Finite Group DatabasebetaFinite Group DatabasebetaOrder 768.
442 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C3×#1810 | C2 | semidirect |
| 3. #71963 | C2 | semidirect |
| 4. #67487 | C2 | semidirect |
| 18. C3×#341 | C22 | semidirect |
| 20. #4549 | C22 | semidirect |
| 23. #1810 | D3 | semidirect |
| 68. #341 | C2×D3 | semidirect |
| 293. C3 | #11895 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#5115 | 2 |
| C3×#1810 | 2 |
| #71963 | 2 |
| #67487 | 2 |
| #11895 | 3 |