Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
273 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 273 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 222. C32 | #2229 | semidirect |
| 254. C3 | #69212 | semidirect |
| 255. C3 | #69356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10590875 | 2 |
| #10590818 | 2 |
| #10589367 | 2 |
| C3×#4505 | 2 |
| C3×#4503 | 2 |
| #10589140 | 2 |
| #10589117 | 2 |
| #69356 | 3 |
| #69212 | 3 |