Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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×#20263333 | C2 | semidirect |
| 2. #27161562 | C2 | semidirect |
| 3. #27161084 | C2 | semidirect |
| 4. #27161080 | C2 | semidirect |
| 5. #27161075 | C2 | semidirect |
| 6. C2×#20263247 | C2 | semidirect |
| 9. C2×#15691342 | C22 | semidirect |
| 10. C22×#13096802 | C22 | semidirect |
| 13. #20263285 | C22 | semidirect |
| 14. C2×C4⋊Dic197 | C22 | semidirect |
| 15. #20263250 | C22 | semidirect |
| 16. #20263250 | C22 | semidirect |
| 17. #20263247 | C22 | semidirect |
| 18. #20263247 | C22 | semidirect |
| 19. #20263247 | C22 | semidirect |
| 21. H(5,𝔽2)×C197 | C4 | semidirect |
| 41. #41×C197 | C2×C4 | semidirect |
| 49. C2×D4×C197 | C2×C4 | semidirect |
| 97. C197 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic197 | semidirect |
| 129. #41 | C2×Dic197 | semidirect |
| 137. C2×D4 | C2×Dic197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263333 | 2 |
| #27161562 | 2 |
| #27161084 | 2 |
| #27161080 | 2 |
| #27161075 | 2 |
| C2×#20263247 | 2 |
| C2×H(5,𝔽2)×C197 | 2 |
| #2897 | 197 |