Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
349 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 349 conjugacy classes of subgroups — too many to draw. Only its 90 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. #10590807 | C2 | semidirect |
| 4. #10589358 | C2 | semidirect |
| 5. C3×#4489 | C2 | semidirect |
| 7. #10589103 | C2 | semidirect |
| 21. #63548 | C4 | semidirect |
| 35. #4489 | D3 | semidirect |
| 43. #3746 | C2×C4 | semidirect |
| 53. C3×C3⋊C16 | C2×C4 | semidirect |
| 143. C3⋊C16 | C4×D3 | semidirect |
| 252. C32 | #2175 | semidirect |
| 291. C3 | #69319 | semidirect |
| 292. C3 | #70884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4872 | 2 |
| #10590807 | 2 |
| C2×#63548 | 2 |
| #10589358 | 2 |
| C3×#4489 | 2 |
| #10589114 | 2 |
| #10589103 | 2 |
| #70884 | 3 |
| #69319 | 3 |