Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
184 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 184 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 81. C83 | #2082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127711 | 2 |
| C2×#14581710 | 2 |
| #19127473 | 2 |
| #19127472 | 2 |
| #19127458 | 2 |
| #430×C83 | 2 |
| #2082 | 83 |