Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
452 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 123 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. #27161878 | C2 | semidirect |
| 2. C2×#20263349 | C2 | semidirect |
| 3. #131×D197 | C2 | semidirect |
| 4. #27161351 | C2 | semidirect |
| 5. #27161350 | C2 | semidirect |
| 6. #27161349 | C2 | semidirect |
| 7. #27161345 | C2 | semidirect |
| 8. #27161344 | C2 | semidirect |
| 9. #108×D197 | C2 | semidirect |
| 10. #27161062 | C2 | semidirect |
| 11. #473×C197 | C2 | semidirect |
| 25. C2×#15691345 | C22 | semidirect |
| 26. C2×D1576 | C22 | semidirect |
| 37. #20263262 | C22 | semidirect |
| 38. #20263261 | C22 | semidirect |
| 39. #20263245 | C22 | semidirect |
| 40. #20263242 | C22 | semidirect |
| 41. #20263242 | C22 | semidirect |
| 43. C2×Q16×C197 | C22 | semidirect |
| 45. #108×C197 | C22 | semidirect |
| 46. #101×C197 | C22 | semidirect |
| 166. C197 | #3067 | semidirect |
| 172. #473 | D197 | semidirect |
| 193. C2×Q16 | C2×D197 | semidirect |
| 209. #108 | C2×D197 | semidirect |
| 211. #101 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161878 | 2 |
| C2×#20263349 | 2 |
| #131×D197 | 2 |
| #27161351 | 2 |
| #27161350 | 2 |
| #27161349 | 2 |
| #27161345 | 2 |
| #27161344 | 2 |
| #108×D197 | 2 |
| #27161062 | 2 |
| #473×C197 | 2 |
| #3067 | 197 |