Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
321 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 321 conjugacy classes of subgroups — too many to draw. Only its 90 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×#4700 | C2 | semidirect |
| 3. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. #10589144 | C2 | semidirect |
| 5. #10589120 | C2 | semidirect |
| 14. #63550 | C4 | semidirect |
| 15. #63547 | C4 | semidirect |
| 16. #63545 | C4 | semidirect |
| 19. #4700 | D3 | semidirect |
| 165. C32 | #2178 | semidirect |
| 190. C3 | #70921 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4700 | 2 |
| #10590629 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| #10589144 | 2 |
| #10589120 | 2 |
| #70921 | 3 |