Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
227 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 227 conjugacy classes of subgroups — too many to draw. Only its 78 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. #10589327 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊C16) | C2 | semidirect |
| 16. C4⋊(C3⋊C16) | D3 | semidirect |
| 177. C32 | #1330 | semidirect |
| 211. C3 | #67557 | semidirect |
| 212. C3 | #67761 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4688 | 2 |
| #10589327 | 2 |
| C3×C4⋊(C3⋊C16) | 2 |
| #67761 | 3 |
| #67557 | 3 |