Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 225 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 225 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. C2×C32×M32 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. #10589373 | C2 | semidirect |
| 18. C2×C3×M32 | D3 | semidirect |
| 68. C2×M32 | C3⋊D3 | semidirect |
| 156. C32 | #2113 | semidirect |
| 186. C3 | #71432 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64110 | 2 |
| C2×C32×M32 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| #10589373 | 2 |
| #71432 | 3 |