Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
454 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782478 | C2 | semidirect |
| 2. #23782471 | C2 | semidirect |
| 3. #23782466 | C2 | semidirect |
| 4. #23781937 | C2 | semidirect |
| 5. #23781932 | C2 | semidirect |
| 6. #23781925 | C2 | semidirect |
| 7. #23781842 | C2 | semidirect |
| 8. #23781837 | C2 | semidirect |
| 9. #23781783 | C2 | semidirect |
| 10. #23781783 | C2 | semidirect |
| 11. #495×C163 | C2 | semidirect |
| 12. #19104783 | C22 | semidirect |
| 16. #19104766 | C22 | semidirect |
| 20. #19104761 | C22 | semidirect |
| 31. #19104741 | C22 | semidirect |
| 32. #19104741 | C22 | semidirect |
| 33. #19104671 | C22 | semidirect |
| 34. #19104671 | C22 | semidirect |
| 36. #19104663 | C22 | semidirect |
| 37. #19104663 | C22 | semidirect |
| 38. #19104654 | C22 | semidirect |
| 39. #19104652 | C22 | semidirect |
| 40. C2×Q16×C163 | C22 | semidirect |
| 41. C2×SD16×C163 | C22 | semidirect |
| 43. #124×C163 | C22 | semidirect |
| 44. C4×C8×C163 | C22 | semidirect |
| 149. C163 | #3290 | semidirect |
| 154. #495 | D163 | semidirect |
| 178. C2×Q16 | C2×D163 | semidirect |
| 180. C2×SD16 | C2×D163 | semidirect |
| 186. #124 | C2×D163 | semidirect |
| 194. C4×C8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782478 | 2 |
| #23782471 | 2 |
| #23782466 | 2 |
| #23781937 | 2 |
| #23781932 | 2 |
| #23781925 | 2 |
| #23781842 | 2 |
| #23781837 | 2 |
| #23781783 | 2 |
| #495×C163 | 2 |
| #3290 | 163 |