Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
130 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 130 conjugacy classes of subgroups — too many to draw. Only its 43 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×#20293790 | C2 | semidirect |
| 2. C2×#20293788 | C2 | semidirect |
| 3. C2×#20293787 | C2 | semidirect |
| 5. #28352177 | C2 | semidirect |
| 6. C4×C431⋊C8 | C2 | semidirect |
| 7. #124×C431 | C2 | semidirect |
| 51. C431 | #495 | semidirect |
| 58. #124 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293790 | 2 |
| C2×#20293788 | 2 |
| C2×#20293787 | 2 |
| C2×#20293785 | 2 |
| #28352177 | 2 |
| C4×C431⋊C8 | 2 |
| #124×C431 | 2 |
| #495 | 431 |