Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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×#14581800 | C2 | semidirect |
| 3. #19127822 | C2 | semidirect |
| 4. #19127817 | C2 | semidirect |
| 5. #19127717 | C2 | semidirect |
| 6. #19127659 | C2 | semidirect |
| 7. #430×C83 | C2 | semidirect |
| 9. #14581825 | C4 | semidirect |
| 10. #14581820 | C4 | semidirect |
| 14. #14581800 | C22 | semidirect |
| 15. #14581800 | C22 | semidirect |
| 20. #14581718 | C22 | semidirect |
| 21. #14581702 | C22 | semidirect |
| 22. C8×Dic83 | C22 | semidirect |
| 25. #108×C83 | C22 | semidirect |
| 90. C83 | #2955 | semidirect |
| 95. #430 | D83 | semidirect |
| 112. #108 | 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×#14581800 | 2 |
| #19127822 | 2 |
| #19127817 | 2 |
| #19127717 | 2 |
| #19127659 | 2 |
| #430×C83 | 2 |
| #2955 | 83 |