Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 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. #19128256 | C2 | semidirect |
| 3. #19128044 | C2 | semidirect |
| 4. #19127983 | C2 | semidirect |
| 5. #19127912 | C2 | semidirect |
| 6. #19127906 | C2 | semidirect |
| 8. #19127795 | C2 | semidirect |
| 9. #19127792 | C2 | semidirect |
| 10. #19127753 | C2 | semidirect |
| 11. #474×C83 | C2 | semidirect |
| 137. C83 | #3107 | semidirect |
| 142. #474 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128256 | 2 |
| C4×#13050589 | 2 |
| #19128044 | 2 |
| #19127983 | 2 |
| #19127912 | 2 |
| #19127906 | 2 |
| #19127864 | 2 |
| #19127795 | 2 |
| #19127792 | 2 |
| #19127753 | 2 |
| #474×C83 | 2 |
| #3107 | 83 |