Finite Group DatabasebetaFinite Group DatabasebetaOrder 27712.
100 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 100 conjugacy classes of subgroups — too many to draw. Only its 37 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×#20294087 | C2 | semidirect |
| 4. #28357155 | C2 | semidirect |
| 5. #28357139 | C2 | semidirect |
| 6. #28357138 | C2 | semidirect |
| 49. C433 | #473 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28357250 | 2 |
| C2×#20294087 | 2 |
| #28357227 | 2 |
| #28357155 | 2 |
| #28357139 | 2 |
| #28357138 | 2 |
| #137×C433 | 2 |
| #473 | 433 |