Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×Dic166 | C2 | semidirect |
| 3. #19128051 | C2 | semidirect |
| 5. #19127986 | C2 | semidirect |
| 7. #19127908 | C2 | semidirect |
| 8. #19127832 | C2 | semidirect |
| 9. #19127806 | C2 | semidirect |
| 117. C83 | #3369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic166 | 2 |
| #19128060 | 2 |
| #19128051 | 2 |
| #19127991 | 2 |
| #19127986 | 2 |
| #19127920 | 2 |
| #19127908 | 2 |
| #19127832 | 2 |
| #19127806 | 2 |
| C4×#13050578 | 2 |
| #556×C83 | 2 |
| #3369 | 83 |