Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
150 conjugacy classes of subgroups; only the 48 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 48 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 |
|---|---|---|
| 1. C2×#20294106 | C2 | semidirect |
| 2. #28357281 | C2 | semidirect |
| 3. #28357280 | C2 | semidirect |
| 52. C433 | #413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20294106 | 2 |
| #28357281 | 2 |
| #28357280 | 2 |
| C2×#20294096 | 2 |
| #413 | 433 |