Finite Group DatabasebetaFinite Group DatabasebetaOrder 10624.
410 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19128232 | C2 | semidirect |
| 2. C2×#14581781 | C2 | semidirect |
| 3. #19128082 | C2 | semidirect |
| 4. #19128057 | C2 | semidirect |
| 5. #19127926 | C2 | semidirect |
| 6. #19127918 | C2 | semidirect |
| 7. #19127857 | C2 | semidirect |
| 8. #19127854 | C2 | semidirect |
| 10. #19127751 | C2 | semidirect |
| 11. #448×C83 | C2 | semidirect |
| 13. C2×#13050580 | C22 | semidirect |
| 17. #14581783 | C22 | semidirect |
| 22. #14581779 | C22 | semidirect |
| 25. #14581757 | C22 | semidirect |
| 27. D4×Dic83 | C22 | semidirect |
| 32. Dic83⋊C8 | C22 | semidirect |
| 33. #14581716 | C22 | semidirect |
| 37. C8×Dic83 | C22 | semidirect |
| 39. C2×SD16×C83 | C22 | semidirect |
| 41. #103×C83 | C22 | semidirect |
| 144. C83 | #3211 | semidirect |
| 153. #448 | D83 | semidirect |
| 160. C2×SD16 | C2×D83 | semidirect |
| 181. #103 | C2×D83 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19128232 | 2 |
| C2×#14581781 | 2 |
| #19128082 | 2 |
| #19128057 | 2 |
| #19127926 | 2 |
| #19127918 | 2 |
| #19127857 | 2 |
| #19127854 | 2 |
| #19127834 | 2 |
| #19127751 | 2 |
| #448×C83 | 2 |
| #3211 | 83 |