Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
307 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 307 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 197. C32 | #1696 | semidirect |
| 228. C3 | #70965 | semidirect |
| 229. C3 | #71380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#4682 | 2 |
| C3×#4679 | 2 |
| #10590310 | 2 |
| #10589323 | 2 |
| #10589095 | 2 |
| #71380 | 3 |
| #70965 | 3 |