Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 3. C2×#14581711 | C2 | semidirect |
| 4. #19127460 | C2 | semidirect |
| 5. #519×C83 | C2 | semidirect |
| 9. #14581781 | C4 | semidirect |
| 80. C83 | #1888 | semidirect |
| 82. #519 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581781 | 2 |
| #19127705 | 2 |
| C2×#14581711 | 2 |
| #19127460 | 2 |
| #519×C83 | 2 |
| #1888 | 83 |