Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
736 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 145 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. #27161915 | C2 | semidirect |
| 2. C2×#20263354 | C2 | semidirect |
| 3. #27161643 | C2 | semidirect |
| 4. #27161254 | C2 | semidirect |
| 5. #27161249 | C2 | semidirect |
| 6. #27161095 | C2 | semidirect |
| 7. #413×C197 | C2 | semidirect |
| 8. #20263374 | C22 | semidirect |
| 12. #20263371 | C22 | semidirect |
| 16. C22×D788 | C22 | semidirect |
| 18. #20263354 | C22 | semidirect |
| 21. #20263322 | C22 | semidirect |
| 22. #20263315 | C22 | semidirect |
| 25. #20263285 | C22 | semidirect |
| 26. #20263252 | C22 | semidirect |
| 28. C2×M16×C197 | C22 | semidirect |
| 29. #101×C197 | C22 | semidirect |
| 30. #100×C197 | C22 | semidirect |
| 38. #15691358 | D4 | semidirect |
| 43. C2×Dic394 | D4 | semidirect |
| 49. C2×D788 | D4 | semidirect |
| 134. C197 | #3021 | semidirect |
| 142. #413 | D197 | semidirect |
| 157. C2×M16 | C2×D197 | semidirect |
| 164. #101 | C2×D197 | semidirect |
| 165. #100 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161915 | 2 |
| C2×#20263354 | 2 |
| #27161643 | 2 |
| #27161254 | 2 |
| #27161249 | 2 |
| #27161095 | 2 |
| #413×C197 | 2 |
| #3021 | 197 |