Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 125 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. #27161894 | C2 | semidirect |
| 2. #27161893 | C2 | semidirect |
| 3. #27161457 | C2 | semidirect |
| 4. #27161354 | C2 | semidirect |
| 5. #27161352 | C2 | semidirect |
| 6. #27161351 | C2 | semidirect |
| 7. #27161262 | C2 | semidirect |
| 8. #27161260 | C2 | semidirect |
| 9. #27161196 | C2 | semidirect |
| 10. #27161194 | C2 | semidirect |
| 11. #578×C197 | C2 | semidirect |
| 146. C197 | #3293 | semidirect |
| 150. #578 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161894 | 2 |
| #27161893 | 2 |
| #27161457 | 2 |
| #27161354 | 2 |
| #27161352 | 2 |
| #27161351 | 2 |
| #27161262 | 2 |
| #27161260 | 2 |
| #27161196 | 2 |
| #27161194 | 2 |
| #578×C197 | 2 |
| #3293 | 197 |