Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
592 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×Q16×D83 | C2 | semidirect |
| 2. C2×SD16×D83 | C2 | semidirect |
| 4. #124×D83 | C2 | semidirect |
| 5. #19128086 | C2 | semidirect |
| 6. #19128085 | C2 | semidirect |
| 7. #19128084 | C2 | semidirect |
| 8. #19128083 | C2 | semidirect |
| 9. #19128082 | C2 | semidirect |
| 10. C4×C8×D83 | C2 | semidirect |
| 11. #495×C83 | C2 | semidirect |
| 14. C2×Dic332 | C22 | semidirect |
| 15. C2×#13050580 | C22 | semidirect |
| 17. C2×#13050579 | C22 | semidirect |
| 18. C2×#13050578 | C22 | semidirect |
| 19. C2×#13050577 | C22 | semidirect |
| 26. #14581781 | C22 | semidirect |
| 27. #14581780 | C22 | semidirect |
| 28. #14581779 | C22 | semidirect |
| 32. C4×C83⋊C8 | C22 | semidirect |
| 33. C8×Dic83 | C22 | semidirect |
| 34. C8×Dic83 | C22 | semidirect |
| 35. C2×Q16×C83 | C22 | semidirect |
| 36. C2×SD16×C83 | C22 | semidirect |
| 38. #124×C83 | C22 | semidirect |
| 39. C4×C8×C83 | C22 | semidirect |
| 125. D83 | #495 | direct (N × H) |
| 127. C83 | C2×#495 | semidirect |
| 137. #495 | D83 | direct (N × H) |
| 144. C2×Q16 | C2×D83 | semidirect |
| 149. C2×SD16 | C2×D83 | semidirect |
| 160. #124 | C2×D83 | semidirect |
| 166. C4×C8 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D83 | 2 |
| C2×SD16×D83 | 2 |
| C2×D8×D83 | 2 |
| #124×D83 | 2 |
| #19128086 | 2 |
| #19128085 | 2 |
| #19128084 | 2 |
| #19128083 | 2 |
| #19128082 | 2 |
| C4×C8×D83 | 2 |
| #495×C83 | 2 |
| C2×#495 | 83 |