Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 161 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. #27161877 | C2 | semidirect |
| 2. #27161653 | C2 | semidirect |
| 3. #27161262 | C2 | semidirect |
| 4. #27161252 | C2 | semidirect |
| 5. #27161096 | C2 | semidirect |
| 6. C2×#20263245 | C2 | semidirect |
| 7. C2×2−1+4×C197 | C2 | semidirect |
| 10. #20263356 | C22 | semidirect |
| 12. #20263351 | C22 | semidirect |
| 15. #20263324 | C22 | semidirect |
| 16. #20263315 | C22 | semidirect |
| 20. #20263253 | C22 | semidirect |
| 21. #20263245 | C22 | semidirect |
| 123. C197 | #3020 | semidirect |
| 125. C2×2−1+4 | D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161877 | 2 |
| #27161653 | 2 |
| #27161262 | 2 |
| #27161252 | 2 |
| #27161096 | 2 |
| C2×#20263245 | 2 |
| C2×2−1+4×C197 | 2 |
| #3020 | 197 |