Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
684 conjugacy classes of subgroups; only the 257 normal subgroups are shown.
This group has 684 conjugacy classes of subgroups — too many to draw. Only its 257 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. #10592805 | C2 | semidirect |
| 3. C22×C3⋊(C3⋊C16) | C2 | semidirect |
| 4. #10589430 | C2 | semidirect |
| 5. #10589428 | C2 | semidirect |
| 9. C32×#135 | C4 | semidirect |
| 47. C3×#135 | Dic3 | semidirect |
| 111. #135 | C3⋊Dic3 | semidirect |
| 172. C32 | #2138 | semidirect |
| 204. C3 | #72077 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#135 | 2 |
| #10592805 | 2 |
| C22×C3⋊(C3⋊C16) | 2 |
| #10589430 | 2 |
| #10589428 | 2 |
| #72077 | 3 |