Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
520 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 157 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×#14581814 | C2 | semidirect |
| 2. #19128212 | C2 | semidirect |
| 3. #19127942 | C2 | semidirect |
| 4. #19127937 | C2 | semidirect |
| 5. #19127930 | C2 | semidirect |
| 6. #19127739 | C2 | semidirect |
| 7. #19127698 | C2 | semidirect |
| 8. C23×C8×C83 | C2 | semidirect |
| 11. C2×Dic332 | C22 | semidirect |
| 12. C2×#13050579 | C22 | semidirect |
| 13. C2×D664 | C22 | semidirect |
| 20. #14581726 | C22 | semidirect |
| 21. #14581724 | C22 | semidirect |
| 22. #14581717 | C22 | semidirect |
| 23. #14581714 | C22 | semidirect |
| 56. C2×C8×C83 | D4 | semidirect |
| 91. C22×C83 | #135 | semidirect |
| 107. C83 | #3050 | semidirect |
| 109. C23×C8 | D83 | semidirect |
| 157. C2×C8 | C22⋊D83 | semidirect |
| 200. C22 | #14581814 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581814 | 2 |
| #19128212 | 2 |
| #19127942 | 2 |
| #19127937 | 2 |
| #19127930 | 2 |
| #19127739 | 2 |
| #19127698 | 2 |
| C23×C8×C83 | 2 |
| #3050 | 83 |