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×#346 | C2 | semidirect |
| 4. #10589367 | C2 | semidirect |
| 5. #10589327 | C2 | semidirect |
| 17. C3×#346 | D3 | semidirect |
| 65. #346 | C3⋊D3 | semidirect |
| 146. C32 | #2163 | semidirect |
| 177. C3 | #69073 | 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×#346 | 2 |
| #10589373 | 2 |
| #10589367 | 2 |
| #10589327 | 2 |
| #69073 | 3 |