Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
849 conjugacy classes of subgroups; only the 324 normal subgroups are shown.
This group has 849 conjugacy classes of subgroups — too many to draw. Only its 324 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 |
|---|---|---|
| 11. C3×#803 | C4 | semidirect |
| 12. #63555 | C4 | semidirect |
| 13. #63553 | C4 | semidirect |
| 45. #803 | Dic3 | semidirect |
| 56. C3×C3⋊C8 | C42 | semidirect |
| 91. C3⋊Dic3 | #97 | semidirect |
| 122. C3⋊C8 | C4×Dic3 | semidirect |
| 155. C32 | C4×#97 | semidirect |
| 184. C3 | Dic3×#97 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×C3⋊Dic3 | 2 |
| C2×C3×#803 | 2 |
| C2×#63555 | 2 |
| C2×#63553 | 2 |
| Dic3×#97 | 3 |