Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 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. #27161732 | C2 | semidirect |
| 2. #27161714 | C2 | semidirect |
| 3. #27161391 | C2 | semidirect |
| 4. #27161356 | C2 | semidirect |
| 5. #27161314 | C2 | semidirect |
| 6. #27161271 | C2 | semidirect |
| 7. #27161214 | C2 | semidirect |
| 8. C4×D1576 | C2 | semidirect |
| 9. C8×D788 | C2 | semidirect |
| 10. #102×D197 | C2 | semidirect |
| 11. #486×C197 | C2 | semidirect |
| 16. C2×#15691343 | C22 | semidirect |
| 17. C2×C8×D197 | C22 | semidirect |
| 20. #20263301 | C22 | semidirect |
| 26. C4×D788 | C22 | semidirect |
| 27. C4⋊C4×D197 | C22 | semidirect |
| 28. #20263260 | C22 | semidirect |
| 29. #20263259 | C22 | semidirect |
| 30. C4⋊#13096802 | C22 | semidirect |
| 32. #20263248 | C22 | semidirect |
| 33. #20263247 | C22 | semidirect |
| 35. #20263238 | C22 | semidirect |
| 36. C4⋊Q8×C197 | C22 | semidirect |
| 38. #102×C197 | C22 | semidirect |
| 39. #102×C197 | C22 | semidirect |
| 40. C4×C8×C197 | C22 | semidirect |
| 88. D788 | D8 | semidirect |
| 89. D788 | #41 | semidirect |
| 142. C197 | #3294 | semidirect |
| 146. #486 | D197 | semidirect |
| 161. C4⋊Q8 | C2×D197 | semidirect |
| 180. #102 | C2×D197 | semidirect |
| 181. #102 | C2×D197 | semidirect |
| 183. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161732 | 2 |
| #27161714 | 2 |
| #27161391 | 2 |
| #27161356 | 2 |
| #27161314 | 2 |
| #27161271 | 2 |
| #27161214 | 2 |
| C4×D1576 | 2 |
| C8×D788 | 2 |
| #102×D197 | 2 |
| #486×C197 | 2 |
| #3294 | 197 |