Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 84 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. #10590891 | C2 | semidirect |
| 3. #10589355 | C2 | semidirect |
| 4. C3×#4489 | C2 | semidirect |
| 5. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 34. #4489 | D3 | semidirect |
| 47. C3×D24 | Q8 | semidirect |
| 126. D24 | Dic6 | semidirect |
| 233. C32 | #2224 | semidirect |
| 271. C3 | #69333 | semidirect |
| 272. C3 | #70886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4872 | 2 |
| #10590891 | 2 |
| #10589355 | 2 |
| C3×#4489 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #10589115 | 2 |
| #10589114 | 2 |
| #70886 | 3 |
| #69333 | 3 |