Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
782 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 782 conjugacy classes of subgroups — too many to draw. Only its 196 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×#5752 | C2 | semidirect |
| 2. #10592839 | C2 | semidirect |
| 3. #10590630 | C2 | semidirect |
| 4. #10590629 | C2 | semidirect |
| 5. C2×#63545 | C2 | semidirect |
| 10. C3×#904 | C22 | semidirect |
| 11. C2×C3×D24 | C22 | semidirect |
| 12. #63639 | C22 | semidirect |
| 13. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 14. #63550 | C22 | semidirect |
| 15. #63547 | C22 | semidirect |
| 16. #63545 | C22 | semidirect |
| 17. #63545 | C22 | semidirect |
| 19. #5752 | D3 | semidirect |
| 48. #904 | C2×D3 | semidirect |
| 49. C2×D24 | C2×D3 | semidirect |
| 168. C32 | #3415 | semidirect |
| 193. C3 | #84007 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#5752 | 2 |
| #10592839 | 2 |
| #10590630 | 2 |
| #10590629 | 2 |
| C2×#63545 | 2 |
| #84007 | 3 |