Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
386 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 386 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. C2×#14581790 | C2 | semidirect |
| 3. #19128092 | C2 | semidirect |
| 4. #19128068 | C2 | semidirect |
| 5. #19127910 | C2 | semidirect |
| 6. #19127904 | C2 | semidirect |
| 7. #19127859 | C2 | semidirect |
| 8. #19127857 | C2 | semidirect |
| 10. #19127755 | C2 | semidirect |
| 138. C83 | #3218 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581790 | 2 |
| #19128232 | 2 |
| #19128092 | 2 |
| #19128068 | 2 |
| #19127910 | 2 |
| #19127904 | 2 |
| #19127859 | 2 |
| #19127857 | 2 |
| #19127839 | 2 |
| #19127755 | 2 |
| #448×C83 | 2 |
| #3218 | 83 |