Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. C4⋊Q8×D197 | C2 | semidirect |
| 3. #27161441 | C2 | semidirect |
| 4. #27161439 | C2 | semidirect |
| 5. #27161438 | C2 | semidirect |
| 6. #27161428 | C2 | semidirect |
| 7. #27161424 | C2 | semidirect |
| 8. #27161079 | C2 | semidirect |
| 9. #27161077 | C2 | semidirect |
| 10. #27161031 | C2 | semidirect |
| 11. #489×C197 | C2 | semidirect |
| 140. C197 | #3141 | semidirect |
| 147. #489 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161628 | 2 |
| C4⋊Q8×D197 | 2 |
| #27161441 | 2 |
| #27161439 | 2 |
| #27161438 | 2 |
| #27161428 | 2 |
| #27161424 | 2 |
| #27161079 | 2 |
| #27161077 | 2 |
| #27161031 | 2 |
| #489×C197 | 2 |
| #3141 | 197 |