Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1038 conjugacy classes of subgroups; only the 209 normal subgroups are shown.
This group has 1038 conjugacy classes of subgroups — too many to draw. Only its 209 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. #10596269 | C2 | semidirect |
| 3. C32×#418 | C2 | semidirect |
| 4. #10592838 | C2 | semidirect |
| 5. #10592705 | C2 | semidirect |
| 6. #10589425 | C2 | semidirect |
| 7. #10589397 | C2 | semidirect |
| 16. C2×#3754 | C4 | semidirect |
| 19. C2×#3753 | C4 | semidirect |
| 28. C3×#418 | D3 | semidirect |
| 47. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 49. C2×#634 | C2×C4 | semidirect |
| 67. C2×C3⋊(C3⋊C8) | C2×C4 | semidirect |
| 120. #418 | C3⋊D3 | semidirect |
| 284. C32 | #1904 | semidirect |
| 340. C3 | #70314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10596269 | 2 |
| C2×#64141 | 2 |
| C32×#418 | 2 |
| #10592838 | 2 |
| #10592705 | 2 |
| #10589425 | 2 |
| #10589397 | 2 |
| #70314 | 3 |