Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
522 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 2. C2×#63655 | C2 | semidirect |
| 4. #10589357 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 17. C3×C4×Q16 | D3 | semidirect |
| 27. C32×Q16 | D4 | semidirect |
| 66. C4×Q16 | C3⋊D3 | semidirect |
| 74. C3×Q16 | D12 | semidirect |
| 92. C32×C4 | SD32 | semidirect |
| 129. Q16 | C4⋊(C3⋊D3) | semidirect |
| 147. C3×C4 | #828 | semidirect |
| 150. C32 | #2207 | semidirect |
| 177. C4 | #63655 | semidirect |
| 180. C3 | #70914 | 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 |
| #10592394 | 2 |
| #10589357 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #70914 | 3 |