Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
369 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 369 conjugacy classes of subgroups — too many to draw. Only its 80 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 |
|---|---|---|
| 1. C3×#4872 | C2 | semidirect |
| 2. #10590864 | C2 | semidirect |
| 3. C2×#63548 | C2 | semidirect |
| 5. #10589358 | C2 | semidirect |
| 6. C3×#4491 | C2 | semidirect |
| 7. Dic3⋊(C3⋊C16) | C2 | semidirect |
| 29. #4872 | D3 | semidirect |
| 36. #4491 | D3 | semidirect |
| 281. C32 | #2210 | semidirect |
| 326. C3 | #69203 | semidirect |
| 327. C3 | #70890 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4872 | 2 |
| #10590864 | 2 |
| C2×#63548 | 2 |
| C2×#63545 | 2 |
| #10589358 | 2 |
| C3×#4491 | 2 |
| Dic3⋊(C3⋊C16) | 2 |
| #70890 | 3 |
| #69203 | 3 |