Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 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. #27161815 | C2 | semidirect |
| 2. #27161790 | C2 | semidirect |
| 3. #27161432 | C2 | semidirect |
| 4. #27161381 | C2 | semidirect |
| 5. #27161371 | C2 | semidirect |
| 6. #27161293 | C2 | semidirect |
| 8. C8×Dic394 | C2 | semidirect |
| 9. C4×#15691347 | C2 | semidirect |
| 10. #27161159 | C2 | semidirect |
| 11. #486×C197 | C2 | semidirect |
| 122. C197 | #3361 | semidirect |
| 127. #486 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161815 | 2 |
| #27161790 | 2 |
| #27161432 | 2 |
| #27161381 | 2 |
| #27161371 | 2 |
| #27161293 | 2 |
| #27161271 | 2 |
| C8×Dic394 | 2 |
| C4×#15691347 | 2 |
| #27161159 | 2 |
| #486×C197 | 2 |
| #3361 | 197 |