Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
309 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 309 conjugacy classes of subgroups — too many to draw. Only its 100 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 |
|---|---|---|
| 3. C3×#4502 | C2 | semidirect |
| 4. C3×Dic3⋊C16 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 7. Dic3×C3⋊C16 | C2 | semidirect |
| 30. #4502 | D3 | semidirect |
| 32. Dic3⋊C16 | D3 | semidirect |
| 253. C32 | #2164 | semidirect |
| 292. C3 | #69074 | semidirect |
| 293. C3 | #69276 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590700 | 2 |
| #10589373 | 2 |
| C3×#4502 | 2 |
| C3×Dic3⋊C16 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589108 | 2 |
| Dic3×C3⋊C16 | 2 |
| #69276 | 3 |
| #69074 | 3 |