Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1565 conjugacy classes of subgroups; only the 436 normal subgroups are shown.
This group has 1565 conjugacy classes of subgroups — too many to draw. Only its 436 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. #10596283 | C2 | semidirect |
| 3. C3×#5812 | C2 | semidirect |
| 4. #10591231 | C2 | semidirect |
| 10. C2×C3×#239 | C4 | semidirect |
| 11. C2×C3×D3×Q8 | C4 | semidirect |
| 24. #5812 | D3 | semidirect |
| 56. C2×#239 | Dic3 | semidirect |
| 57. C2×D3×Q8 | Dic3 | semidirect |
| 236. C32 | #2884 | semidirect |
| 276. C3 | #82556 | semidirect |
| 277. C3 | #84119 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#1007 | 2 |
| #10596283 | 2 |
| C3×#5812 | 2 |
| #10591231 | 2 |
| #84119 | 3 |
| #82556 | 3 |