Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
778 conjugacy classes of subgroups; only the 293 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 293 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. C2×#14581799 | C2 | semidirect |
| 2. #19128184 | C2 | semidirect |
| 3. #19127706 | C2 | semidirect |
| 4. #19127702 | C2 | semidirect |
| 5. #19127697 | C2 | semidirect |
| 6. C2×#14581713 | C2 | semidirect |
| 9. C2×#13050574 | C22 | semidirect |
| 10. C22×C83⋊C8 | C22 | semidirect |
| 13. #14581751 | C22 | semidirect |
| 14. C2×C4⋊Dic83 | C22 | semidirect |
| 15. #14581716 | C22 | semidirect |
| 16. #14581716 | C22 | semidirect |
| 17. #14581713 | C22 | semidirect |
| 18. #14581713 | C22 | semidirect |
| 19. #14581713 | C22 | semidirect |
| 21. H(5,𝔽2)×C83 | C4 | semidirect |
| 41. #41×C83 | C2×C4 | semidirect |
| 49. C2×D4×C83 | C2×C4 | semidirect |
| 98. C83 | #2897 | semidirect |
| 107. H(5,𝔽2) | Dic83 | semidirect |
| 129. #41 | C2×Dic83 | semidirect |
| 137. C2×D4 | C2×Dic83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581799 | 2 |
| #19128184 | 2 |
| #19127706 | 2 |
| #19127702 | 2 |
| #19127697 | 2 |
| C2×#14581713 | 2 |
| C2×H(5,𝔽2)×C83 | 2 |
| #2897 | 83 |