Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D197 | C2 | semidirect |
| 2. C2×#20263358 | C2 | semidirect |
| 4. #27161234 | C2 | semidirect |
| 5. #27161233 | C2 | semidirect |
| 6. #27161220 | C2 | semidirect |
| 7. #27161219 | C2 | semidirect |
| 8. #27161218 | C2 | semidirect |
| 9. #27161086 | C2 | semidirect |
| 10. #27161041 | C2 | semidirect |
| 11. #451×C197 | C2 | semidirect |
| 23. C2×#15691348 | C22 | semidirect |
| 24. C2×#15691347 | C22 | semidirect |
| 25. C2×#15691345 | C22 | semidirect |
| 35. #20263251 | C22 | semidirect |
| 36. #20263250 | C22 | semidirect |
| 37. #20263249 | C22 | semidirect |
| 41. C2×Q16×C197 | C22 | semidirect |
| 43. #103×C197 | C22 | semidirect |
| 58. Q8×D197 | D4 | semidirect |
| 141. C22×C197 | #137 | semidirect |
| 152. C2×D197 | #137 | semidirect |
| 169. C197 | #3004 | semidirect |
| 176. #451 | D197 | semidirect |
| 195. C2×Q16 | C2×D197 | semidirect |
| 211. #103 | C2×D197 | semidirect |
| 321. C22 | #20263358 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D197 | 2 |
| C2×#20263358 | 2 |
| #27161592 | 2 |
| #27161234 | 2 |
| #27161233 | 2 |
| #27161220 | 2 |
| #27161219 | 2 |
| #27161218 | 2 |
| #27161086 | 2 |
| #27161041 | 2 |
| #451×C197 | 2 |
| #3004 | 197 |