Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
2214 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 2214 conjugacy classes of subgroups — too many to draw. Only its 565 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 |
|---|---|---|
| 2. C32×#568 | C2 | semidirect |
| 3. #41×C3⋊Dic3 | C2 | semidirect |
| 4. #10592838 | C2 | semidirect |
| 5. C2×#63652 | C2 | semidirect |
| 8. #64367 | C4 | semidirect |
| 9. #64366 | C4 | semidirect |
| 15. C2×C32×M16 | C22 | semidirect |
| 18. #64135 | C22 | semidirect |
| 19. C2×C4×C3⋊Dic3 | C22 | semidirect |
| 20. #63652 | C22 | semidirect |
| 21. #63652 | C22 | semidirect |
| 23. C3×#568 | D3 | semidirect |
| 40. #3828 | C2×C4 | semidirect |
| 42. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 44. C2×#634 | C2×C4 | semidirect |
| 62. C2×C3×M16 | C2×D3 | semidirect |
| 91. #568 | C3⋊D3 | semidirect |
| 140. C2×M16 | C2×C3⋊D3 | semidirect |
| 209. C32 | #2901 | semidirect |
| 246. C3 | #83817 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596756 | 2 |
| C32×#568 | 2 |
| #41×C3⋊Dic3 | 2 |
| #10592838 | 2 |
| C2×#63652 | 2 |
| #83817 | 3 |