Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
526 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 123 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×#20263349 | C2 | semidirect |
| 2. C2×D8×D197 | C2 | semidirect |
| 3. #27161722 | C2 | semidirect |
| 4. #27161317 | C2 | semidirect |
| 5. #27161312 | C2 | semidirect |
| 6. #27161291 | C2 | semidirect |
| 7. #27161228 | C2 | semidirect |
| 8. #27161223 | C2 | semidirect |
| 9. C4×D1576 | C2 | semidirect |
| 10. C8×D788 | C2 | semidirect |
| 11. #495×C197 | C2 | semidirect |
| 12. C2×#15691359 | C22 | semidirect |
| 15. C2×#15691345 | C22 | semidirect |
| 20. C2×C8×D197 | C22 | semidirect |
| 24. #20263297 | C22 | semidirect |
| 27. C4×D788 | C22 | semidirect |
| 29. #20263260 | C22 | semidirect |
| 30. C4⋊#13096802 | C22 | semidirect |
| 31. #20263250 | C22 | semidirect |
| 32. #20263248 | C22 | semidirect |
| 33. #20263247 | C22 | semidirect |
| 35. #20263238 | C22 | semidirect |
| 36. C2×Q16×C197 | C22 | semidirect |
| 37. C2×SD16×C197 | C22 | semidirect |
| 39. #124×C197 | C22 | semidirect |
| 40. C4×C8×C197 | C22 | semidirect |
| 56. D1576 | D4 | semidirect |
| 127. C2×D197 | #135 | semidirect |
| 143. C197 | #3280 | semidirect |
| 148. #495 | D197 | semidirect |
| 159. C2×Q16 | C2×D197 | semidirect |
| 161. C2×SD16 | C2×D197 | semidirect |
| 168. #124 | C2×D197 | semidirect |
| 184. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20263349 | 2 |
| C2×D8×D197 | 2 |
| #27161722 | 2 |
| #27161317 | 2 |
| #27161312 | 2 |
| #27161291 | 2 |
| #27161228 | 2 |
| #27161223 | 2 |
| C4×D1576 | 2 |
| C8×D788 | 2 |
| #495×C197 | 2 |
| #3280 | 197 |