Finite Group DatabasebetaFinite Group DatabasebetaOrder 29248.
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. #28410545 | C2 | semidirect |
| 2. #28410545 | C2 | semidirect |
| 3. #28410538 | C2 | semidirect |
| 4. #28410536 | C2 | semidirect |
| 5. #28410535 | C2 | semidirect |
| 6. #28410534 | C2 | semidirect |
| 7. #28410531 | C2 | semidirect |
| 8. #28410529 | C2 | semidirect |
| 10. C4×C22⋊D457 | C2 | semidirect |
| 11. #28410512 | C2 | semidirect |
| 12. #28410511 | C2 | semidirect |
| 13. #28410508 | C2 | semidirect |
| 14. C2×C22⋊Dic457 | C2 | semidirect |
| 15. C2×C22⋊C4×C457 | C2 | semidirect |
| 16. C2×Dic914 | C22 | semidirect |
| 22. C2×C4×D457 | C22 | semidirect |
| 23. C4⋊Dic457 | C22 | semidirect |
| 24. C4⋊Dic457 | C22 | semidirect |
| 25. C4⋊Dic457 | C22 | semidirect |
| 26. #20300720 | C22 | semidirect |
| 27. #20300720 | C22 | semidirect |
| 28. #20300720 | C22 | semidirect |
| 29. #20300720 | C22 | semidirect |
| 30. #20300720 | C22 | semidirect |
| 38. #20300718 | C22 | semidirect |
| 39. #20300718 | C22 | semidirect |
| 40. #20300718 | C22 | semidirect |
| 41. C4×Dic457 | C22 | semidirect |
| 42. C4×Dic457 | C22 | semidirect |
| 43. C4×Dic457 | C22 | semidirect |
| 110. C457 | #551 | semidirect |
| 126. C2×C22⋊C4 | D457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #28410545 | 2 |
| #28410538 | 2 |
| #28410536 | 2 |
| #28410535 | 2 |
| #28410534 | 2 |
| #28410531 | 2 |
| #28410529 | 2 |
| #28410521 | 2 |
| C4×C22⋊D457 | 2 |
| #28410512 | 2 |
| #28410511 | 2 |
| #28410508 | 2 |
| C2×C22⋊Dic457 | 2 |
| C2×C22⋊C4×C457 | 2 |
| #551 | 457 |