Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 133 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×#20263346 | C2 | semidirect |
| 2. C22×#15691341 | C2 | semidirect |
| 3. #27161591 | C2 | semidirect |
| 4. #27161586 | C2 | semidirect |
| 5. #27161336 | C2 | semidirect |
| 6. #27161331 | C2 | semidirect |
| 7. #27161328 | C2 | semidirect |
| 8. #27161324 | C2 | semidirect |
| 9. #27161115 | C2 | semidirect |
| 10. #27161076 | C2 | semidirect |
| 11. #416×C197 | C2 | semidirect |
| 15. C2×#15691348 | C22 | semidirect |
| 16. C2×#15691346 | C22 | semidirect |
| 17. C2×#15691345 | C22 | semidirect |
| 18. C2×#15691343 | C22 | semidirect |
| 34. #20263259 | C22 | semidirect |
| 35. #20263257 | C22 | semidirect |
| 36. #20263251 | C22 | semidirect |
| 37. #20263248 | C22 | semidirect |
| 41. #103×C197 | C22 | semidirect |
| 42. #102×C197 | C22 | semidirect |
| 63. C2×#13096802 | D4 | semidirect |
| 148. C197 | #3054 | semidirect |
| 160. #416 | D197 | semidirect |
| 189. #103 | C2×D197 | semidirect |
| 191. #102 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263346 | 2 |
| C22×#15691341 | 2 |
| #27161591 | 2 |
| #27161586 | 2 |
| #27161336 | 2 |
| #27161331 | 2 |
| #27161328 | 2 |
| #27161324 | 2 |
| #27161115 | 2 |
| #27161076 | 2 |
| #416×C197 | 2 |
| #3054 | 197 |