Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
277 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 277 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 224. C32 | #2229 | semidirect |
| 256. C3 | #69297 | semidirect |
| 257. C3 | #69356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590873 | 2 |
| #10590807 | 2 |
| #10589369 | 2 |
| C3×#4505 | 2 |
| C3×Dic3⋊C16 | 2 |
| #10589139 | 2 |
| #10589119 | 2 |
| #69356 | 3 |
| #69297 | 3 |