Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
213 conjugacy classes of subgroups; only the 64 normal subgroups are shown.
This group has 213 conjugacy classes of subgroups — too many to draw. Only its 64 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. C3×#4504 | C2 | semidirect |
| 3. C2×C3×C3⋊C32 | C2 | semidirect |
| 9. #63626 | C4 | semidirect |
| 17. #4504 | D3 | semidirect |
| 18. C2×C3⋊C32 | D3 | semidirect |
| 137. C32 | #1415 | semidirect |
| 165. C3 | #67577 | semidirect |
| 166. C3 | #67596 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63626 | 2 |
| C3×#4504 | 2 |
| C2×C3×C3⋊C32 | 2 |
| #67596 | 3 |
| #67577 | 3 |