Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
| 3. #27161429 | C2 | semidirect |
| 4. #27161419 | C2 | semidirect |
| 5. #27161360 | C2 | semidirect |
| 6. #27161317 | C2 | semidirect |
| 7. #27161240 | C2 | semidirect |
| 8. C4×#15691345 | C2 | semidirect |
| 9. #27161144 | C2 | semidirect |
| 10. #27161074 | C2 | semidirect |
| 11. #462×C197 | C2 | semidirect |
| 125. C197 | #3302 | semidirect |
| 133. #462 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161802 | 2 |
| #27161732 | 2 |
| #27161429 | 2 |
| #27161419 | 2 |
| #27161360 | 2 |
| #27161317 | 2 |
| #27161240 | 2 |
| C4×#15691345 | 2 |
| #27161144 | 2 |
| #27161074 | 2 |
| #462×C197 | 2 |
| #3302 | 197 |