Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#20263351 | C2 | semidirect |
| 2. C22×#15691343 | C2 | semidirect |
| 3. #27161643 | C2 | semidirect |
| 4. #27161224 | C2 | semidirect |
| 5. #27161213 | C2 | semidirect |
| 6. #27161084 | C2 | semidirect |
| 7. #27161075 | C2 | semidirect |
| 8. #27161046 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C197 | C2 | semidirect |
| 10. C22×D788 | C22 | semidirect |
| 12. C2×#15691345 | C22 | semidirect |
| 14. C2×#15691343 | C22 | semidirect |
| 15. C2×#15691343 | C22 | semidirect |
| 16. C2×#15691342 | C22 | semidirect |
| 17. C22×#13096802 | C22 | semidirect |
| 20. #20263300 | C22 | semidirect |
| 22. #20263285 | C22 | semidirect |
| 23. #20263250 | C22 | semidirect |
| 24. #20263247 | C22 | semidirect |
| 25. #20263247 | C22 | semidirect |
| 26. C22⋊#13096802 | C22 | semidirect |
| 32. C2×#41×C197 | C22 | semidirect |
| 36. C22×D4×C197 | C22 | semidirect |
| 62. #41×C197 | D4 | semidirect |
| 76. C2×D4×C197 | D4 | semidirect |
| 151. C197 | #3008 | semidirect |
| 153. C2×H(5,𝔽2) | D197 | semidirect |
| 167. C2×#41 | C2×D197 | semidirect |
| 172. C22×D4 | C2×D197 | semidirect |
| 198. #41 | C22⋊D197 | semidirect |
| 217. C2×D4 | C22⋊D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263351 | 2 |
| C22×#15691343 | 2 |
| #27161643 | 2 |
| #27161224 | 2 |
| #27161213 | 2 |
| #27161084 | 2 |
| #27161075 | 2 |
| #27161046 | 2 |
| C2×H(5,𝔽2)×C197 | 2 |
| #3008 | 197 |