Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
214 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 99 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. #28352184 | C2 | semidirect |
| 2. #28352180 | C2 | semidirect |
| 3. #28352180 | C2 | semidirect |
| 5. #28352165 | C2 | semidirect |
| 6. Q8×Dic431 | C2 | semidirect |
| 8. #28352147 | C2 | semidirect |
| 9. #28352145 | C2 | semidirect |
| 10. C2×C4⋊Dic431 | C2 | semidirect |
| 11. C22⋊Q8×C431 | C2 | semidirect |
| 72. C431 | #552 | semidirect |
| 79. C22⋊Q8 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352184 | 2 |
| #28352180 | 2 |
| #28352173 | 2 |
| #28352165 | 2 |
| Q8×Dic431 | 2 |
| C4×C22⋊D431 | 2 |
| #28352147 | 2 |
| #28352145 | 2 |
| C2×C4⋊Dic431 | 2 |
| C22⋊Q8×C431 | 2 |
| #552 | 431 |