Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #19128426 | C2 | semidirect |
| 4. #19128053 | C2 | semidirect |
| 5. #19128007 | C2 | semidirect |
| 7. #19127912 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 9. #19127795 | C2 | semidirect |
| 116. C83 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128426 | 2 |
| #19128421 | 2 |
| #19128054 | 2 |
| #19128053 | 2 |
| #19128007 | 2 |
| #19127922 | 2 |
| #19127912 | 2 |
| #19127825 | 2 |
| #19127795 | 2 |
| C4×#13050578 | 2 |
| #474×C83 | 2 |
| #3364 | 83 |