Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
573 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 573 conjugacy classes of subgroups — too many to draw. Only its 148 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 |
|---|---|---|
| 2. C2×C3×#812 | C2 | semidirect |
| 3. #10589110 | C2 | semidirect |
| 18. C2×#812 | D3 | semidirect |
| 217. C32 | #2115 | semidirect |
| 253. C3 | #71435 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64110 | 2 |
| C2×C3×#812 | 2 |
| #10589110 | 2 |
| #71435 | 3 |