Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
356 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 356 conjugacy classes of subgroups — too many to draw. Only its 121 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. #19128424 | C2 | semidirect |
| 2. #19128095 | C2 | semidirect |
| 4. #19127924 | C2 | semidirect |
| 6. #19127912 | C2 | semidirect |
| 7. #19127803 | C2 | semidirect |
| 8. C4×Dic332 | C2 | semidirect |
| 9. #446×C83 | C2 | semidirect |
| 103. C83 | #3402 | semidirect |
| 110. #446 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128424 | 2 |
| #19128095 | 2 |
| #19128085 | 2 |
| #19127924 | 2 |
| #19127917 | 2 |
| #19127912 | 2 |
| #19127803 | 2 |
| C4×Dic332 | 2 |
| #446×C83 | 2 |
| #3402 | 83 |