Finite Group DatabasebetaFinite Group DatabasebetaOrder 29504.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #28414111 | C2 | semidirect |
| 2. #28414111 | C2 | semidirect |
| 3. #28414104 | C2 | semidirect |
| 4. #28414102 | C2 | semidirect |
| 5. #28414101 | C2 | semidirect |
| 6. #28414100 | C2 | semidirect |
| 7. #28414097 | C2 | semidirect |
| 8. #28414095 | C2 | semidirect |
| 10. C4×C22⋊D461 | C2 | semidirect |
| 11. #28414078 | C2 | semidirect |
| 12. #28414077 | C2 | semidirect |
| 13. #28414074 | C2 | semidirect |
| 14. C2×C22⋊Dic461 | C2 | semidirect |
| 15. C2×C22⋊C4×C461 | C2 | semidirect |
| 16. C2×Dic922 | C22 | semidirect |
| 22. C2×C4×D461 | C22 | semidirect |
| 23. C4⋊Dic461 | C22 | semidirect |
| 24. C4⋊Dic461 | C22 | semidirect |
| 25. C4⋊Dic461 | C22 | semidirect |
| 26. #20301480 | C22 | semidirect |
| 27. #20301480 | C22 | semidirect |
| 28. #20301480 | C22 | semidirect |
| 29. #20301480 | C22 | semidirect |
| 30. #20301480 | C22 | semidirect |
| 38. #20301478 | C22 | semidirect |
| 39. #20301478 | C22 | semidirect |
| 40. #20301478 | C22 | semidirect |
| 41. C4×Dic461 | C22 | semidirect |
| 42. C4×Dic461 | C22 | semidirect |
| 43. C4×Dic461 | C22 | semidirect |
| 110. C461 | #551 | semidirect |
| 126. C2×C22⋊C4 | D461 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28414111 | 2 |
| #28414104 | 2 |
| #28414102 | 2 |
| #28414101 | 2 |
| #28414100 | 2 |
| #28414097 | 2 |
| #28414095 | 2 |
| #28414087 | 2 |
| C4×C22⋊D461 | 2 |
| #28414078 | 2 |
| #28414077 | 2 |
| #28414074 | 2 |
| C2×C22⋊Dic461 | 2 |
| C2×C22⋊C4×C461 | 2 |
| #551 | 461 |