Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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×#20293787 | C2 | semidirect |
| 2. C22×C431⋊C8 | C2 | semidirect |
| 4. #28352120 | C2 | semidirect |
| 5. #28352113 | C2 | semidirect |
| 6. #28352109 | C2 | semidirect |
| 7. C22⋊Q8×C431 | C2 | semidirect |
| 27. C431⋊C8 | D4 | semidirect |
| 39. C22×C431 | SD16 | semidirect |
| 55. C431 | #465 | semidirect |
| 59. C22⋊Q8 | D431 | semidirect |
| 98. C22 | #20293787 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293787 | 2 |
| C22×C431⋊C8 | 2 |
| #28352163 | 2 |
| #28352120 | 2 |
| #28352113 | 2 |
| #28352109 | 2 |
| C22⋊Q8×C431 | 2 |
| #465 | 431 |