Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
321 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 96 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×#4901 | C2 | semidirect |
| 3. C16×C3⋊Dic3 | C2 | semidirect |
| 4. #10589135 | C2 | semidirect |
| 5. #10589111 | C2 | semidirect |
| 19. #4901 | D3 | semidirect |
| 167. C32 | #2170 | semidirect |
| 192. C3 | #71452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4901 | 2 |
| #10590921 | 2 |
| C16×C3⋊Dic3 | 2 |
| #10589135 | 2 |
| #10589111 | 2 |
| #71452 | 3 |