Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
738 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 143 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. C22×Q8×D83 | C2 | semidirect |
| 2. C2×#14581821 | C2 | semidirect |
| 4. #19127859 | C2 | semidirect |
| 5. #19127858 | C2 | semidirect |
| 6. #19127857 | C2 | semidirect |
| 7. #19127839 | C2 | semidirect |
| 8. #19127838 | C2 | semidirect |
| 9. #19127708 | C2 | semidirect |
| 10. #19127663 | C2 | semidirect |
| 11. #448×C83 | C2 | semidirect |
| 23. C2×Dic332 | C22 | semidirect |
| 24. C2×#13050580 | C22 | semidirect |
| 25. C2×#13050578 | C22 | semidirect |
| 35. #14581717 | C22 | semidirect |
| 36. #14581716 | C22 | semidirect |
| 37. #14581715 | C22 | semidirect |
| 41. C2×SD16×C83 | C22 | semidirect |
| 43. #103×C83 | C22 | semidirect |
| 59. Q8×D83 | D4 | semidirect |
| 144. C22×C83 | #137 | semidirect |
| 152. C2×D83 | #137 | semidirect |
| 170. C83 | #3004 | semidirect |
| 179. #448 | D83 | semidirect |
| 197. C2×SD16 | C2×D83 | semidirect |
| 211. #103 | C2×D83 | semidirect |
| 321. C22 | #14581821 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D83 | 2 |
| C2×#14581821 | 2 |
| #19128211 | 2 |
| #19127859 | 2 |
| #19127858 | 2 |
| #19127857 | 2 |
| #19127839 | 2 |
| #19127838 | 2 |
| #19127708 | 2 |
| #19127663 | 2 |
| #448×C83 | 2 |
| #3004 | 83 |