Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
199 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 199 conjugacy classes of subgroups — too many to draw. Only its 50 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. #10589332 | C2 | semidirect |
| 3. C3×#4466 | C2 | semidirect |
| 19. #4466 | D3 | semidirect |
| 146. C32 | #1355 | semidirect |
| 172. C3 | #67520 | semidirect |
| 173. C3 | #67783 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4713 | 2 |
| #10589332 | 2 |
| C3×#4466 | 2 |
| #67783 | 3 |
| #67520 | 3 |