Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
462 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#20263285 | C2 | semidirect |
| 2. #27161400 | C2 | semidirect |
| 3. #27161395 | C2 | semidirect |
| 4. #27161390 | C2 | semidirect |
| 5. #27161119 | C2 | semidirect |
| 6. #27161084 | C2 | semidirect |
| 7. #27161043 | C2 | semidirect |
| 13. #20263285 | C22 | semidirect |
| 14. C2×C4⋊Dic197 | C22 | semidirect |
| 15. C2×C4⋊Dic197 | C22 | semidirect |
| 18. #20263259 | C22 | semidirect |
| 19. #20263257 | C22 | semidirect |
| 20. #20263247 | C22 | semidirect |
| 21. #20263247 | C22 | semidirect |
| 22. C22⋊#13096802 | C22 | semidirect |
| 23. C22⋊#13096802 | C22 | semidirect |
| 125. C197 | #3094 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263285 | 2 |
| #27161400 | 2 |
| #27161395 | 2 |
| #27161390 | 2 |
| #27161119 | 2 |
| #27161084 | 2 |
| #27161043 | 2 |
| C2×#121×C197 | 2 |
| #3094 | 197 |