Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
374 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 193. C32 | #1663 | semidirect |
| 217. C3 | #71252 | semidirect |
| 218. C3 | #71961 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C3⋊#564 | 2 |
| C3×#5069 | 2 |
| #10590315 | 2 |
| #10589409 | 2 |
| #10589088 | 2 |
| #71961 | 3 |
| #71252 | 3 |