Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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 |
|---|---|---|
| 2. C2×#14581798 | C2 | semidirect |
| 3. #19127824 | C2 | semidirect |
| 4. #19127819 | C2 | semidirect |
| 5. #19127750 | C2 | semidirect |
| 6. #19127719 | C2 | semidirect |
| 7. #405×C83 | C2 | semidirect |
| 9. #14581825 | C4 | semidirect |
| 10. #14581820 | C4 | semidirect |
| 14. #14581798 | C22 | semidirect |
| 15. #14581798 | C22 | semidirect |
| 19. #14581728 | C22 | semidirect |
| 20. #14581720 | C22 | semidirect |
| 24. #97×C83 | C22 | semidirect |
| 25. C4×C8×C83 | C22 | semidirect |
| 90. C83 | #2955 | semidirect |
| 97. #405 | D83 | semidirect |
| 114. #97 | C2×D83 | semidirect |
| 115. C4×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128501 | 2 |
| C2×#14581798 | 2 |
| #19127824 | 2 |
| #19127819 | 2 |
| #19127750 | 2 |
| #19127719 | 2 |
| #405×C83 | 2 |
| #2955 | 83 |