Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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×#15691357 | C2 | semidirect |
| 2. C2×#20263347 | C2 | semidirect |
| 3. #27161592 | C2 | semidirect |
| 4. #27161238 | C2 | semidirect |
| 5. #27161234 | C2 | semidirect |
| 6. #27161225 | C2 | semidirect |
| 7. #27161220 | C2 | semidirect |
| 8. #27161213 | C2 | semidirect |
| 9. #27161072 | C2 | semidirect |
| 10. C22⋊C8×D197 | C2 | semidirect |
| 11. #450×C197 | C2 | semidirect |
| 12. C2×#15691359 | C22 | semidirect |
| 23. C2×#15691348 | C22 | semidirect |
| 24. C2×#15691347 | C22 | semidirect |
| 25. C2×#15691343 | C22 | semidirect |
| 26. C2×C8×D197 | C22 | semidirect |
| 28. #20263302 | C22 | semidirect |
| 29. #20263301 | C22 | semidirect |
| 34. #20263284 | C22 | semidirect |
| 35. #20263251 | C22 | semidirect |
| 36. #20263249 | C22 | semidirect |
| 37. #20263247 | C22 | semidirect |
| 39. #20263238 | C22 | semidirect |
| 41. C2×SD16×C197 | C22 | semidirect |
| 43. #102×C197 | C22 | semidirect |
| 52. #15691357 | D4 | semidirect |
| 147. C22×C197 | #135 | semidirect |
| 175. C197 | #3002 | semidirect |
| 182. #450 | D197 | semidirect |
| 202. C2×SD16 | C2×D197 | semidirect |
| 217. #102 | C2×D197 | semidirect |
| 333. C22 | #20263347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15691357 | 2 |
| C2×#20263347 | 2 |
| #27161592 | 2 |
| #27161238 | 2 |
| #27161234 | 2 |
| #27161225 | 2 |
| #27161220 | 2 |
| #27161213 | 2 |
| #27161072 | 2 |
| C22⋊C8×D197 | 2 |
| #450×C197 | 2 |
| #3002 | 197 |