Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
374 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19128425 | C2 | semidirect |
| 3. #19128038 | C2 | semidirect |
| 4. #19128028 | C2 | semidirect |
| 5. #19127983 | C2 | semidirect |
| 6. #19127978 | C2 | semidirect |
| 7. #19127948 | C2 | semidirect |
| 8. C4×#13050579 | C2 | semidirect |
| 9. #19127780 | C2 | semidirect |
| 10. #19127742 | C2 | semidirect |
| 11. #500×C83 | C2 | semidirect |
| 98. C8×C83 | #41 | semidirect |
| 123. C83 | #3353 | semidirect |
| 126. #500 | D83 | semidirect |
| 222. C8 | #13050591 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128425 | 2 |
| #19128354 | 2 |
| #19128038 | 2 |
| #19128028 | 2 |
| #19127983 | 2 |
| #19127978 | 2 |
| #19127948 | 2 |
| C4×#13050579 | 2 |
| #19127780 | 2 |
| #19127742 | 2 |
| #500×C83 | 2 |
| #3353 | 83 |