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. #10596224 | C2 | semidirect |
| 2. #10596223 | C2 | semidirect |
| 3. C32×#504 | C2 | semidirect |
| 4. #10592608 | C2 | semidirect |
| 5. #10592607 | C2 | semidirect |
| 6. #10592603 | C2 | semidirect |
| 7. C2×#63627 | C2 | semidirect |
| 14. C2×#3746 | C22 | semidirect |
| 16. #64113 | C22 | semidirect |
| 18. C32×M32 | C22 | semidirect |
| 19. C2×C32×C16 | C22 | semidirect |
| 20. #63628 | C22 | semidirect |
| 21. #63627 | C22 | semidirect |
| 22. #63627 | C22 | semidirect |
| 23. #63627 | C22 | semidirect |
| 24. #63626 | C22 | semidirect |
| 27. C3×#504 | D3 | semidirect |
| 63. C3×M32 | C2×D3 | semidirect |
| 64. C2×C3×C16 | C2×D3 | semidirect |
| 93. #504 | C3⋊D3 | semidirect |
| 137. M32 | C2×C3⋊D3 | semidirect |
| 138. C2×C16 | C2×C3⋊D3 | semidirect |
| 189. C32 | #3416 | semidirect |
| 219. C3 | #82014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596224 | 2 |
| #10596223 | 2 |
| C32×#504 | 2 |
| #10592608 | 2 |
| #10592607 | 2 |
| #10592603 | 2 |
| C2×#63627 | 2 |
| #82014 | 3 |