Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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×#20293800 | C2 | semidirect |
| 2. #28352209 | C2 | direct (N × H) |
| 3. C2×#20293790 | C2 | semidirect |
| 4. C2×#20293788 | C2 | semidirect |
| 5. C2×#20293787 | C2 | semidirect |
| 6. C2×#20293785 | C2 | semidirect |
| 7. C22×C431⋊C8 | C2 | semidirect |
| 8. C2×#41×C431 | C2 | semidirect |
| 10. #20293800 | C22 | semidirect |
| 15. #20293790 | C22 | semidirect |
| 16. #20293788 | C22 | semidirect |
| 17. #20293787 | C22 | semidirect |
| 18. #20293785 | C22 | semidirect |
| 21. C2×C431⋊C8 | C22 | semidirect |
| 23. #41×C431 | C22 | semidirect |
| 66. C2×C431 | #135 | semidirect |
| 69. C431 | C2×#135 | semidirect |
| 72. C2×#41 | D431 | semidirect |
| 82. #41 | C2×D431 | semidirect |
| 137. C2 | #28352209 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293800 | 2 |
| #28352209 | 2 |
| C2×#20293790 | 2 |
| C2×#20293788 | 2 |
| C2×#20293787 | 2 |
| C2×#20293785 | 2 |
| C22×C431⋊C8 | 2 |
| C2×#41×C431 | 2 |
| C2×#135 | 431 |