Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
224 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 12. #14581727 | C4 | semidirect |
| 13. #14581725 | C4 | semidirect |
| 14. #14581723 | C4 | semidirect |
| 16. #14581703 | C4 | semidirect |
| 80. C83 | #1773 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581727 | 2 |
| #19127737 | 2 |
| #19127659 | 2 |
| #19127657 | 2 |
| C2×#14581703 | 2 |
| #19127461 | 2 |
| #339×C83 | 2 |
| #1773 | 83 |