Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
520 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 520 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×#20263349 | C2 | semidirect |
| 2. C22×C8×D197 | C2 | semidirect |
| 3. #27161592 | C2 | semidirect |
| 4. #27161317 | C2 | semidirect |
| 5. #27161316 | C2 | semidirect |
| 6. #27161315 | C2 | semidirect |
| 7. #27161311 | C2 | semidirect |
| 8. #27161310 | C2 | semidirect |
| 9. #27161116 | C2 | semidirect |
| 10. #27161074 | C2 | semidirect |
| 11. #467×C197 | C2 | semidirect |
| 15. C2×#15691345 | C22 | semidirect |
| 16. C2×D1576 | C22 | semidirect |
| 31. #20263260 | C22 | semidirect |
| 32. #20263257 | C22 | semidirect |
| 33. #20263250 | C22 | semidirect |
| 34. #20263248 | C22 | semidirect |
| 35. #20263246 | C22 | semidirect |
| 36. C2×Q16×C197 | C22 | semidirect |
| 39. #107×C197 | C22 | semidirect |
| 40. #103×C197 | C22 | semidirect |
| 64. C8×D197 | D4 | semidirect |
| 118. C22×C197 | #135 | semidirect |
| 129. C2×D197 | #135 | semidirect |
| 145. C197 | #3050 | semidirect |
| 151. #467 | D197 | semidirect |
| 161. C2×Q16 | C2×D197 | semidirect |
| 181. #107 | C2×D197 | semidirect |
| 184. #103 | C2×D197 | semidirect |
| 274. C22 | #20263349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| C22×C8×D197 | 2 |
| #27161592 | 2 |
| #27161317 | 2 |
| #27161316 | 2 |
| #27161315 | 2 |
| #27161311 | 2 |
| #27161310 | 2 |
| #27161116 | 2 |
| #27161074 | 2 |
| #467×C197 | 2 |
| #3050 | 197 |