Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
373 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 373 conjugacy classes of subgroups — too many to draw. Only its 104 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 |
|---|---|---|
| 14. C3×#803 | C4 | semidirect |
| 15. C3×C4×C3⋊C8 | C4 | semidirect |
| 57. #803 | Dic3 | semidirect |
| 58. C4×C3⋊C8 | Dic3 | semidirect |
| 219. C32 | #1288 | semidirect |
| 259. C3 | #67666 | semidirect |
| 260. C3 | #67752 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592636 | 2 |
| C3×#4926 | 2 |
| C3×C4×#208 | 2 |
| #67752 | 3 |
| #67666 | 3 |