Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1236 conjugacy classes of subgroups; only the 345 normal subgroups are shown.
This group has 1236 conjugacy classes of subgroups — too many to draw. Only its 345 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. C2×C32×#125 | C2 | semidirect |
| 3. #10592767 | C2 | direct (N × H) |
| 4. C2×#63637 | C2 | semidirect |
| 6. C2×C4×C3⋊(C3⋊C8) | C2 | semidirect |
| 11. C32×#125 | C22 | semidirect |
| 19. #63637 | C22 | semidirect |
| 21. C4×C3⋊(C3⋊C8) | C22 | semidirect |
| 22. C2×C3×#125 | D3 | semidirect |
| 51. C3×#125 | C2×D3 | semidirect |
| 80. C2×#125 | C3⋊D3 | semidirect |
| 120. #125 | C2×C3⋊D3 | semidirect |
| 148. C2×C32 | #488 | semidirect |
| 182. C32 | C2×#488 | semidirect |
| 201. C2×C3 | #5068 | semidirect |
| 216. C3 | C2×#5068 | semidirect |
| 218. C2 | #10592767 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#125 | 2 |
| C2×#64084 | 2 |
| #10592767 | 2 |
| C2×#63637 | 2 |
| C2×#63636 | 2 |
| C2×C4×C3⋊(C3⋊C8) | 2 |
| C2×#5068 | 3 |