Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
388 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 77 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. C22⋊C8×D83 | C2 | semidirect |
| 3. #95×D83 | C2 | semidirect |
| 4. #19127436 | C2 | semidirect |
| 5. #19127435 | C2 | semidirect |
| 6. #19127434 | C2 | semidirect |
| 7. #327×C83 | C2 | semidirect |
| 9. C2×D4×D83 | C4 | semidirect |
| 13. #14581767 | C4 | semidirect |
| 17. #14581763 | C4 | semidirect |
| 18. C4⋊C4×D83 | C4 | semidirect |
| 20. C22⋊(C83⋊C8) | C22 | semidirect |
| 23. C83⋊#95 | C22 | semidirect |
| 25. C22⋊C8×C83 | C22 | semidirect |
| 26. #95×C83 | C22 | semidirect |
| 30. C2×D332 | C2×C4 | semidirect |
| 50. C4⋊Dic83 | C2×C4 | semidirect |
| 56. C2×D4×C83 | C2×C4 | semidirect |
| 60. C4⋊C4×C83 | C2×C4 | semidirect |
| 141. D83 | #327 | direct (N × H) |
| 143. C83 | C2×#327 | semidirect |
| 150. #327 | D83 | direct (N × H) |
| 166. C22⋊C8 | C2×D83 | semidirect |
| 169. #95 | C2×D83 | semidirect |
| 181. C2×D4 | C4×D83 | semidirect |
| 200. C4⋊C4 | C4×D83 | semidirect |