Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1332 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 1332 conjugacy classes of subgroups — too many to draw. Only its 241 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. C32×#518 | C2 | semidirect |
| 3. C2×#63660 | C2 | semidirect |
| 4. #10592700 | C2 | semidirect |
| 5. #10589398 | C2 | semidirect |
| 14. #64149 | C4 | semidirect |
| 19. C3×#518 | D3 | semidirect |
| 38. C2×C4⋊(C3⋊D3) | C2×C4 | semidirect |
| 39. C32×C4⋊C4 | D4 | semidirect |
| 44. C4×C3⋊Dic3 | C2×C4 | semidirect |
| 85. #518 | C3⋊D3 | semidirect |
| 104. C3×C4⋊C4 | #67 | semidirect |
| 188. C4⋊C4 | #638 | semidirect |
| 210. C32 | #1887 | semidirect |
| 256. C3 | #71650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#518 | 2 |
| C2×#64149 | 2 |
| C2×#63660 | 2 |
| #10592700 | 2 |
| #10589398 | 2 |
| #71650 | 3 |