Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#20263353 | C2 | semidirect |
| 2. #27161630 | C2 | semidirect |
| 3. C4×D4×D197 | C2 | semidirect |
| 4. #27161297 | C2 | semidirect |
| 5. #27161296 | C2 | semidirect |
| 6. #27161281 | C2 | semidirect |
| 7. #27161275 | C2 | semidirect |
| 8. #27161274 | C2 | semidirect |
| 9. #27161101 | C2 | semidirect |
| 10. #27161079 | C2 | semidirect |
| 11. #461×C197 | C2 | semidirect |
| 20. #20263323 | C22 | semidirect |
| 21. #20263315 | C22 | semidirect |
| 34. C4⋊#13096802 | C22 | semidirect |
| 35. #20263255 | C22 | semidirect |
| 36. #20263250 | C22 | semidirect |
| 37. #20263248 | C22 | semidirect |
| 38. #20263246 | C22 | semidirect |
| 40. C4⋊Q8×C197 | C22 | semidirect |
| 42. C4⋊C8×C197 | C22 | semidirect |
| 43. #103×C197 | C22 | semidirect |
| 54. D4×D197 | D4 | semidirect |
| 146. C4×C197 | AGL(1,ℤ/8) | semidirect |
| 160. C197 | #3036 | semidirect |
| 168. #461 | D197 | semidirect |
| 182. C4⋊Q8 | C2×D197 | semidirect |
| 200. C4⋊C8 | C2×D197 | semidirect |
| 202. #103 | C2×D197 | semidirect |
| 311. C4 | #20263353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263353 | 2 |
| #27161630 | 2 |
| C4×D4×D197 | 2 |
| #27161297 | 2 |
| #27161296 | 2 |
| #27161281 | 2 |
| #27161275 | 2 |
| #27161274 | 2 |
| #27161101 | 2 |
| #27161079 | 2 |
| #461×C197 | 2 |
| #3036 | 197 |