Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 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×#20263345 | C2 | semidirect |
| 2. #27161723 | C2 | semidirect |
| 3. #27161462 | C2 | semidirect |
| 4. #27161320 | C2 | semidirect |
| 5. #27161312 | C2 | semidirect |
| 6. #27161292 | C2 | semidirect |
| 7. #27161230 | C2 | semidirect |
| 8. #27161221 | C2 | semidirect |
| 9. D8×Dic197 | C2 | semidirect |
| 10. C8×C22⋊D197 | C2 | semidirect |
| 11. C22×D8×C197 | C2 | semidirect |
| 12. C2×#15691357 | C22 | semidirect |
| 14. C2×Dic788 | C22 | semidirect |
| 15. C2×#15691346 | C22 | semidirect |
| 16. C2×#15691346 | C22 | semidirect |
| 17. C2×C8×D197 | C22 | semidirect |
| 18. #20263313 | C22 | semidirect |
| 22. #20263297 | C22 | semidirect |
| 24. D4×Dic197 | C22 | semidirect |
| 27. #20263260 | C22 | semidirect |
| 28. #20263255 | C22 | semidirect |
| 29. #20263251 | C22 | semidirect |
| 30. #20263247 | C22 | semidirect |
| 31. #20263247 | C22 | semidirect |
| 33. #20263238 | C22 | semidirect |
| 34. C8×Dic197 | C22 | semidirect |
| 76. D8×C197 | D4 | semidirect |
| 123. C22×C197 | #135 | semidirect |
| 143. C197 | #3280 | semidirect |
| 146. C22×D8 | D197 | semidirect |
| 206. D8 | C22⋊D197 | semidirect |
| 270. C22 | #20263345 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263345 | 2 |
| #27161723 | 2 |
| #27161462 | 2 |
| #27161320 | 2 |
| #27161312 | 2 |
| #27161292 | 2 |
| #27161230 | 2 |
| #27161221 | 2 |
| D8×Dic197 | 2 |
| C8×C22⋊D197 | 2 |
| C22×D8×C197 | 2 |
| #3280 | 197 |