Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 4. #19127456 | C2 | semidirect |
| 5. #19127455 | C2 | semidirect |
| 6. #19127455 | C2 | semidirect |
| 7. #336×C83 | C2 | semidirect |
| 11. C2×#13050573 | C4 | semidirect |
| 16. C2×C8×D83 | C4 | semidirect |
| 109. C83 | #1729 | semidirect |
| 116. #336 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13050573 | 2 |
| C22×C8×D83 | 2 |
| C2×#14581749 | 2 |
| #19127456 | 2 |
| #19127455 | 2 |
| #336×C83 | 2 |
| #1729 | 83 |