Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
341 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 341 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 4. C3×#4493 | C2 | semidirect |
| 5. #10589143 | C2 | semidirect |
| 25. #4493 | D3 | semidirect |
| 157. C3⋊D3 | #368 | semidirect |
| 189. C32 | C2×#368 | semidirect |
| 221. C3 | D3×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3⋊D3×#108 | 2 |
| #10590913 | 2 |
| C2×#63542 | 2 |
| C3×#4493 | 2 |
| #10589143 | 2 |
| D3×#368 | 3 |