Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
397 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 397 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 213. C32 | #2089 | semidirect |
| 249. C3 | #70532 | semidirect |
| 250. C3 | #70626 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#818 | 2 |
| C3×#5102 | 2 |
| #10591139 | 2 |
| #10589418 | 2 |
| #10589167 | 2 |
| #70626 | 3 |
| #70532 | 3 |