Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
120 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 51 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. C4×Dic862 | C2 | semidirect |
| 3. #28352122 | C2 | semidirect |
| 4. #28352112 | C2 | semidirect |
| 6. #28352100 | C2 | semidirect |
| 9. #20293788 | C4 | semidirect |
| 21. Dic862 | C2×C4 | semidirect |
| 25. C431⋊C8 | C2×C4 | semidirect |
| 49. C431 | #440 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293788 | 2 |
| C4×Dic862 | 2 |
| #28352122 | 2 |
| #28352112 | 2 |
| #28352110 | 2 |
| #28352100 | 2 |
| C4×D4×C431 | 2 |
| #440 | 431 |