Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
181 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 181 conjugacy classes of subgroups — too many to draw. Only its 66 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. C2×C3⋊(C3⋊C32) | C2 | semidirect |
| 3. C3×#4504 | C2 | semidirect |
| 10. C3×D48 | C4 | semidirect |
| 15. #4504 | D3 | semidirect |
| 37. D48 | Dic3 | semidirect |
| 126. C32 | #1415 | semidirect |
| 153. C3 | #67577 | semidirect |
| 154. C3 | #67824 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D48 | 2 |
| C2×C3⋊(C3⋊C32) | 2 |
| C3×#4504 | 2 |
| #67824 | 3 |
| #67577 | 3 |