Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
568 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 205 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. #19127568 | C2 | semidirect |
| 3. #19127565 | C2 | semidirect |
| 6. C4×Dic83⋊C4 | C2 | semidirect |
| 8. #19127547 | C2 | semidirect |
| 9. #376×C83 | C2 | semidirect |
| 19. C42×D83 | C4 | semidirect |
| 99. C83 | #2283 | semidirect |
| 108. #376 | D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×D83 | 2 |
| #19127568 | 2 |
| #19127565 | 2 |
| #19127563 | 2 |
| #19127560 | 2 |
| C4×Dic83⋊C4 | 2 |
| C4×(C2×D83)⋊C4 | 2 |
| #19127547 | 2 |
| #376×C83 | 2 |
| #2283 | 83 |