Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 285 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 285 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. C32×#576 | C2 | semidirect |
| 2. #10596224 | C2 | semidirect |
| 3. #10592894 | C2 | semidirect |
| 4. #10592893 | C2 | semidirect |
| 5. C2×#63654 | C2 | semidirect |
| 6. #10592846 | C2 | semidirect |
| 7. #10592839 | C2 | semidirect |
| 16. C2×#3746 | C22 | semidirect |
| 17. #64113 | C22 | semidirect |
| 18. #63656 | C22 | semidirect |
| 19. #63655 | C22 | semidirect |
| 20. #63654 | C22 | semidirect |
| 21. #63654 | C22 | semidirect |
| 22. #63653 | C22 | semidirect |
| 23. #63639 | C22 | semidirect |
| 24. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 25. C3×#576 | D3 | semidirect |
| 88. #576 | C3⋊D3 | semidirect |
| 189. C32 | #3416 | semidirect |
| 219. C3 | #84008 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#576 | 2 |
| #10596224 | 2 |
| #10592894 | 2 |
| #10592893 | 2 |
| C2×#63654 | 2 |
| #10592846 | 2 |
| #10592839 | 2 |
| #84008 | 3 |