Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
384 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 384 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. #19128437 | C2 | semidirect |
| 2. #19128436 | C2 | semidirect |
| 3. #19128082 | C2 | semidirect |
| 5. #19127918 | C2 | semidirect |
| 6. #19127915 | C2 | semidirect |
| 7. #19127902 | C2 | semidirect |
| 8. #19127825 | C2 | semidirect |
| 9. C4×#13050580 | C2 | semidirect |
| 10. #19127781 | C2 | semidirect |
| 11. #460×C83 | C2 | semidirect |
| 128. C83 | #3396 | semidirect |
| 136. #460 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128437 | 2 |
| #19128436 | 2 |
| #19128082 | 2 |
| #19128077 | 2 |
| #19127918 | 2 |
| #19127915 | 2 |
| #19127902 | 2 |
| #19127825 | 2 |
| C4×#13050580 | 2 |
| #19127781 | 2 |
| #460×C83 | 2 |
| #3396 | 83 |