Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
224 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 75 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×#14581728 | C2 | semidirect |
| 5. #19127656 | C2 | semidirect |
| 6. #19127461 | C2 | semidirect |
| 7. #336×C83 | C2 | semidirect |
| 14. #14581717 | C4 | semidirect |
| 15. #14581717 | C4 | semidirect |
| 16. #14581714 | C4 | semidirect |
| 17. #14581714 | C4 | semidirect |
| 106. C83 | #1929 | semidirect |
| 113. #336 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581728 | 2 |
| C2×#14581720 | 2 |
| #19127698 | 2 |
| #19127667 | 2 |
| #19127656 | 2 |
| #19127461 | 2 |
| #336×C83 | 2 |
| #1929 | 83 |