Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 conjugacy classes of subgroups — too many to draw. Only its 545 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. #19128537 | C2 | semidirect |
| 2. #19128518 | C2 | semidirect |
| 3. #19128513 | C2 | semidirect |
| 4. #19128506 | C2 | semidirect |
| 5. #19128501 | C2 | semidirect |
| 6. C2×#14581814 | C2 | semidirect |
| 7. C2×#131×C83 | C2 | semidirect |
| 9. #14581839 | C22 | semidirect |
| 10. #14581838 | C22 | semidirect |
| 12. C2×#13050590 | C22 | semidirect |
| 14. #14581825 | C22 | semidirect |
| 15. #14581820 | C22 | semidirect |
| 16. #14581814 | C22 | semidirect |
| 17. #14581814 | C22 | semidirect |
| 18. #14581814 | C22 | semidirect |
| 19. #14581814 | C22 | semidirect |
| 20. C2×Dic332 | C22 | semidirect |
| 21. C2×#13050579 | C22 | semidirect |
| 22. C2×D664 | C22 | semidirect |
| 24. #131×C83 | C22 | semidirect |
| 25. #131×C83 | C22 | semidirect |
| 26. C2×M16×C83 | C22 | semidirect |
| 27. C22×C8×C83 | C22 | semidirect |
| 90. C83 | #3584 | semidirect |
| 97. C2×#131 | D83 | semidirect |
| 114. #131 | C2×D83 | semidirect |
| 115. #131 | C2×D83 | semidirect |
| 116. C2×M16 | C2×D83 | semidirect |
| 117. C22×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128537 | 2 |
| #19128518 | 2 |
| #19128513 | 2 |
| #19128506 | 2 |
| #19128501 | 2 |
| C2×#14581814 | 2 |
| C2×#131×C83 | 2 |
| #3584 | 83 |