Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #27161634 | C2 | semidirect |
| 3. #27161446 | C2 | semidirect |
| 4. #27161442 | C2 | semidirect |
| 5. #27161441 | C2 | semidirect |
| 6. #27161439 | C2 | semidirect |
| 7. #27161438 | C2 | semidirect |
| 8. #27161074 | C2 | semidirect |
| 9. #27161072 | C2 | semidirect |
| 10. #97×D197 | C2 | semidirect |
| 11. #489×C197 | C2 | semidirect |
| 137. C197 | #3135 | semidirect |
| 146. #489 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161634 | 2 |
| #27161628 | 2 |
| #27161446 | 2 |
| #27161442 | 2 |
| #27161441 | 2 |
| #27161439 | 2 |
| #27161438 | 2 |
| #27161074 | 2 |
| #27161072 | 2 |
| #97×D197 | 2 |
| #489×C197 | 2 |
| #3135 | 197 |