Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
222 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 222 conjugacy classes of subgroups — too many to draw. Only its 63 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. #19127749 | C2 | semidirect |
| 4. C83⋊#338 | C2 | semidirect |
| 5. #430×C83 | C2 | semidirect |
| 66. C83 | #2091 | semidirect |
| 68. #430 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19127749 | 2 |
| #19127664 | 2 |
| C83⋊#338 | 2 |
| #430×C83 | 2 |
| #2091 | 83 |