Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161802 | C2 | semidirect |
| 2. Q8×D788 | C2 | semidirect |
| 3. #27161439 | C2 | semidirect |
| 4. #27161430 | C2 | semidirect |
| 5. #27161375 | C2 | semidirect |
| 6. #27161360 | C2 | semidirect |
| 8. #27161285 | C2 | semidirect |
| 9. #27161181 | C2 | semidirect |
| 11. #446×C197 | C2 | semidirect |
| 122. C197 | #3367 | semidirect |
| 132. #446 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161802 | 2 |
| Q8×D788 | 2 |
| #27161439 | 2 |
| #27161430 | 2 |
| #27161375 | 2 |
| #27161360 | 2 |
| #27161295 | 2 |
| #27161285 | 2 |
| #27161181 | 2 |
| C4×D1576 | 2 |
| #446×C197 | 2 |
| #3367 | 197 |