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×#578 | C2 | semidirect |
| 2. #10596223 | C2 | semidirect |
| 3. #10592893 | C2 | semidirect |
| 4. #10592892 | C2 | semidirect |
| 5. #10592878 | C2 | semidirect |
| 6. C2×#63655 | C2 | semidirect |
| 7. #10592839 | C2 | semidirect |
| 12. C32×#135 | C22 | semidirect |
| 13. C2×C32×Q16 | C22 | semidirect |
| 18. #63656 | C22 | semidirect |
| 19. #63655 | C22 | semidirect |
| 20. #63655 | C22 | semidirect |
| 21. #63654 | C22 | semidirect |
| 22. #63653 | C22 | semidirect |
| 23. #63639 | C22 | semidirect |
| 24. C2×C3⋊(C3⋊C16) | C22 | semidirect |
| 25. C3×#578 | D3 | semidirect |
| 57. C3×#135 | C2×D3 | semidirect |
| 58. C2×C3×Q16 | C2×D3 | semidirect |
| 87. #578 | C3⋊D3 | semidirect |
| 128. #135 | C2×C3⋊D3 | semidirect |
| 129. C2×Q16 | C2×C3⋊D3 | semidirect |
| 189. C32 | #3416 | semidirect |
| 219. C3 | #84016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#578 | 2 |
| #10596223 | 2 |
| #10592893 | 2 |
| #10592892 | 2 |
| #10592878 | 2 |
| C2×#63655 | 2 |
| #10592839 | 2 |
| #84016 | 3 |