Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
112 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 112 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
|---|---|---|
| 3. Q8×Dic431 | C2 | semidirect |
| 4. Dic431⋊C8 | C2 | semidirect |
| 5. #28352113 | C2 | semidirect |
| 7. C2×Q16×C431 | C2 | semidirect |
| 51. C431 | #464 | semidirect |
| 53. C2×Q16 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20293787 | 2 |
| #28352178 | 2 |
| Q8×Dic431 | 2 |
| Dic431⋊C8 | 2 |
| #28352113 | 2 |
| #28352111 | 2 |
| C2×Q16×C431 | 2 |
| #464 | 431 |