Finite Group DatabasebetaFinite Group DatabasebetaOrder 27584.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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. #28352188 | C2 | semidirect |
| 2. #28352187 | C2 | semidirect |
| 3. #28352184 | C2 | semidirect |
| 4. #28352184 | C2 | semidirect |
| 5. #28352182 | C2 | semidirect |
| 6. #28352182 | C2 | semidirect |
| 7. #28352180 | C2 | semidirect |
| 8. #28352179 | C2 | semidirect |
| 12. #28352168 | C2 | semidirect |
| 13. #28352167 | C2 | semidirect |
| 14. #28352165 | C2 | semidirect |
| 15. C22⋊Q8×C431 | C2 | semidirect |
| 97. C431 | #563 | semidirect |
| 113. C22⋊Q8 | D431 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28352188 | 2 |
| #28352187 | 2 |
| #28352184 | 2 |
| #28352182 | 2 |
| #28352180 | 2 |
| #28352179 | 2 |
| #28352175 | 2 |
| #28352172 | 2 |
| #28352171 | 2 |
| #28352168 | 2 |
| #28352167 | 2 |
| #28352165 | 2 |
| C22⋊Q8×C431 | 2 |
| #563 | 431 |