Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 89 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. #19127711 | C2 | semidirect |
| 4. C2×#14581710 | C2 | semidirect |
| 5. #19127473 | C2 | semidirect |
| 6. C83⋊#338 | C2 | semidirect |
| 11. C2×#13050580 | C4 | semidirect |
| 12. C2×#13050578 | C4 | semidirect |
| 108. C83 | #1902 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14581822 | 2 |
| #19127718 | 2 |
| #19127711 | 2 |
| C2×#14581710 | 2 |
| #19127473 | 2 |
| C83⋊#338 | 2 |
| #568×C83 | 2 |
| #1902 | 83 |