Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
305 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 305 conjugacy classes of subgroups — too many to draw. Only its 124 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. C4×C3⋊(C3⋊C16) | C2 | semidirect |
| 3. C3×#4461 | C2 | semidirect |
| 4. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 24. #4461 | D3 | semidirect |
| 187. C32 | #2164 | semidirect |
| 216. C3 | #69074 | semidirect |
| 217. C3 | #69883 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4689 | 2 |
| C4×C3⋊(C3⋊C16) | 2 |
| C3×#4461 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| (C2×D3)⋊(C3⋊C16) | 2 |
| #69883 | 3 |
| #69074 | 3 |