Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
773 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 773 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. C2×C3×#904 | C2 | semidirect |
| 2. C2×#63639 | C2 | semidirect |
| 3. #10590636 | C2 | semidirect |
| 4. #10590630 | C2 | semidirect |
| 5. #10590629 | C2 | semidirect |
| 9. C2×C3×Dic12 | C22 | semidirect |
| 13. C3×#904 | C22 | semidirect |
| 14. C2×C3×D24 | C22 | semidirect |
| 16. #63639 | C22 | semidirect |
| 17. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 18. #63550 | C22 | semidirect |
| 19. #63547 | C22 | semidirect |
| 20. #63545 | C22 | semidirect |
| 22. C2×#904 | D3 | semidirect |
| 62. C2×Dic12 | C2×D3 | semidirect |
| 66. #904 | C2×D3 | semidirect |
| 67. C2×D24 | C2×D3 | semidirect |
| 249. C32 | #3414 | semidirect |
| 287. C3 | #83894 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#904 | 2 |
| C2×#63639 | 2 |
| #10590636 | 2 |
| #10590630 | 2 |
| #10590629 | 2 |
| #83894 | 3 |