Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1080 conjugacy classes of subgroups; only the 265 normal subgroups are shown.
This group has 1080 conjugacy classes of subgroups — too many to draw. Only its 265 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×C43 | C2 | semidirect |
| 3. C2×#63632 | C2 | semidirect |
| 4. #10592623 | C2 | semidirect |
| 12. #64084 | C4 | semidirect |
| 13. #64083 | C4 | semidirect |
| 15. #64078 | C4 | semidirect |
| 19. C3×C43 | D3 | semidirect |
| 37. C32×C42 | D4 | semidirect |
| 77. C43 | C3⋊D3 | semidirect |
| 93. C3×C42 | D12 | semidirect |
| 105. C32×C4 | #104 | semidirect |
| 164. C42 | C4⋊(C3⋊D3) | semidirect |
| 172. C3×C4 | #805 | semidirect |
| 177. C32 | #1962 | semidirect |
| 209. C4 | #63632 | semidirect |
| 213. C3 | #69395 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10595948 | 2 |
| C32×C43 | 2 |
| C2×#63632 | 2 |
| #10592623 | 2 |
| #69395 | 3 |