Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
430 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 119 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. #27161630 | C2 | semidirect |
| 2. C4×#15691357 | C2 | semidirect |
| 3. #27161406 | C2 | semidirect |
| 4. #27161361 | C2 | semidirect |
| 5. #27161280 | C2 | semidirect |
| 6. #27161274 | C2 | semidirect |
| 7. #27161225 | C2 | semidirect |
| 8. #27161188 | C2 | semidirect |
| 9. #27161178 | C2 | semidirect |
| 10. #27161135 | C2 | semidirect |
| 11. #474×C197 | C2 | semidirect |
| 86. Dic394 | #41 | semidirect |
| 109. D4×C197 | #41 | semidirect |
| 144. C197 | #3115 | semidirect |
| 150. #474 | D197 | semidirect |
| 241. D4 | #15691359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161630 | 2 |
| C4×#15691357 | 2 |
| #27161406 | 2 |
| #27161361 | 2 |
| #27161280 | 2 |
| #27161274 | 2 |
| #27161225 | 2 |
| #27161188 | 2 |
| #27161178 | 2 |
| #27161135 | 2 |
| #474×C197 | 2 |
| #3115 | 197 |