Finite Group DatabasebetaFinite Group DatabasebetaOrder 25216.
462 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 462 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. #27161790 | C2 | semidirect |
| 3. #27161396 | C2 | semidirect |
| 4. #27161366 | C2 | semidirect |
| 5. #27161307 | C2 | semidirect |
| 6. #27161276 | C2 | semidirect |
| 7. #27161231 | C2 | semidirect |
| 8. C4×#15691347 | C2 | semidirect |
| 9. C8×D788 | C2 | semidirect |
| 10. #102×D197 | C2 | semidirect |
| 11. #486×C197 | C2 | semidirect |
| 15. C2×#15691346 | C22 | semidirect |
| 16. C2×C8×D197 | C22 | semidirect |
| 18. #20263306 | C22 | semidirect |
| 23. C4×Dic394 | C22 | semidirect |
| 27. C4⋊C4×D197 | C22 | semidirect |
| 28. #20263258 | C22 | semidirect |
| 29. #20263257 | C22 | semidirect |
| 30. C4⋊#13096802 | C22 | semidirect |
| 31. #20263251 | 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 |
| 85. D788 | SD16 | semidirect |
| 136. C197 | #3295 | semidirect |
| 140. #486 | D197 | semidirect |
| 154. C4⋊Q8 | C2×D197 | semidirect |
| 174. #102 | C2×D197 | semidirect |
| 175. #102 | C2×D197 | semidirect |
| 177. C4×C8 | C2×D197 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #27161790 | 2 |
| #27161714 | 2 |
| #27161396 | 2 |
| #27161366 | 2 |
| #27161307 | 2 |
| #27161276 | 2 |
| #27161231 | 2 |
| C4×#15691347 | 2 |
| C8×D788 | 2 |
| #102×D197 | 2 |
| #486×C197 | 2 |
| #3295 | 197 |