Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
323 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 323 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 186. C32 | #1593 | semidirect |
| 216. C3 | #68089 | semidirect |
| 217. C3 | #70906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C4×Dic12 | 2 |
| #10590258 | 2 |
| #10589323 | 2 |
| C3×#4455 | 2 |
| #10589084 | 2 |
| #70906 | 3 |
| #68089 | 3 |