Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
474 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 137 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×#63656 | C2 | semidirect |
| 5. #10589358 | C2 | semidirect |
| 7. C4⋊(C3⋊(C3⋊C16)) | C2 | semidirect |
| 22. C3×C4×Q16 | D3 | semidirect |
| 82. C4×Q16 | C3⋊D3 | semidirect |
| 181. C32 | #2211 | semidirect |
| 213. C3 | #70915 | 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×#63656 | 2 |
| C2×#63655 | 2 |
| #10592395 | 2 |
| #10589358 | 2 |
| #10589357 | 2 |
| C4⋊(C3⋊(C3⋊C16)) | 2 |
| #70915 | 3 |