Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
486 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 157 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×C4×Q16 | C2 | semidirect |
| 4. #10589430 | C2 | semidirect |
| 6. #10589356 | C2 | semidirect |
| 7. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 16. #63655 | C4 | direct (N × H) |
| 21. C3×C4×Q16 | D3 | semidirect |
| 32. C32×Q16 | C2×C4 | semidirect |
| 44. C3⋊(C3⋊C16) | C2×C4 | semidirect |
| 74. C4×Q16 | C3⋊D3 | semidirect |
| 84. C3×Q16 | C4×D3 | semidirect |
| 104. C32×C4 | SD32 | semidirect |
| 143. Q16 | C4×C3⋊D3 | semidirect |
| 163. C3×C4 | #828 | semidirect |
| 167. C32 | C4×SD32 | semidirect |
| 195. C4 | #63655 | direct (N × H) |
| 198. C3 | C4×#828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×C4×Q16 | 2 |
| C2×#63655 | 2 |
| C4×#3745 | 2 |
| #10589430 | 2 |
| #10589357 | 2 |
| #10589356 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| C4×#828 | 3 |