Finite Group DatabasebetaFinite Group DatabasebetaOrder 1536.
1016 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 225 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. #10713447 | C2 | semidirect |
| 3. #10688988 | C2 | semidirect |
| 4. C3×#11402 | C2 | semidirect |
| 19. #11402 | D3 | semidirect |
| 168. C3×C8 | #361 | semidirect |
| 226. C8 | #4516 | semidirect |
| 244. C3 | #141754 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#68062 | 2 |
| #10713447 | 2 |
| #10688988 | 2 |
| C3×#11402 | 2 |
| #141754 | 3 |