Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
536 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 2. #19127717 | C2 | semidirect |
| 3. #19127711 | C2 | semidirect |
| 4. #19127675 | C2 | semidirect |
| 5. #413×C83 | C2 | semidirect |
| 8. C2×#13050590 | C4 | semidirect |
| 12. C22×Dic166 | C4 | semidirect |
| 109. C83 | #1796 | semidirect |
| 113. #413 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581839 | 2 |
| #19127717 | 2 |
| #19127711 | 2 |
| #19127675 | 2 |
| #413×C83 | 2 |
| #1796 | 83 |