Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
641 conjugacy classes of subgroups; only the 196 normal subgroups are shown.
This group has 641 conjugacy classes of subgroups — too many to draw. Only its 196 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. C8×C3⋊Dic3 | C4 | semidirect |
| 13. #63576 | C4 | semidirect |
| 61. C3⋊(C3⋊C8) | C42 | semidirect |
| 100. C3⋊Dic3 | #107 | semidirect |
| 180. C32 | C4×#107 | semidirect |
| 218. C3 | #68785 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊Dic3 | 2 |
| #10591274 | 2 |
| C2×#63576 | 2 |
| C3×#4551 | 2 |
| #68785 | 3 |