Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
456 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. C32×C4⋊C16 | C2 | semidirect |
| 4. #10589368 | C2 | semidirect |
| 5. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 17. C3×C4⋊C16 | D3 | semidirect |
| 65. C4⋊C16 | C3⋊D3 | semidirect |
| 151. C32 | #2163 | semidirect |
| 183. C3 | #69275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C8×C3⋊D3 | 2 |
| C32×C4⋊C16 | 2 |
| #10589373 | 2 |
| #10589368 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #69275 | 3 |