Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
713 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 713 conjugacy classes of subgroups — too many to draw. Only its 224 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 |
|---|---|---|
| 13. #63572 | C4 | semidirect |
| 108. C3⋊Dic3 | #97 | semidirect |
| 190. C32 | #1767 | semidirect |
| 229. C3 | #69809 | 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×#63572 | 2 |
| #10589156 | 2 |
| #69809 | 3 |