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. #27161394 | C2 | semidirect |
| 4. #27161371 | C2 | semidirect |
| 5. #27161280 | C2 | semidirect |
| 6. #27161279 | C2 | semidirect |
| 7. #27161219 | C2 | semidirect |
| 8. #27161182 | C2 | semidirect |
| 9. #27161178 | C2 | semidirect |
| 10. #27161135 | C2 | semidirect |
| 11. #477×C197 | C2 | semidirect |
| 87. Dic394 | #41 | semidirect |
| 108. Q8×C197 | #41 | semidirect |
| 140. C197 | #3112 | semidirect |
| 146. #477 | D197 | semidirect |
| 231. Q8 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161630 | 2 |
| C4×Q8×D197 | 2 |
| #27161394 | 2 |
| #27161371 | 2 |
| #27161280 | 2 |
| #27161279 | 2 |
| #27161219 | 2 |
| #27161182 | 2 |
| #27161178 | 2 |
| #27161135 | 2 |
| #477×C197 | 2 |
| #3112 | 197 |