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. #23782474 | C2 | semidirect |
| 3. #23782470 | C2 | semidirect |
| 4. #23782050 | C2 | semidirect |
| 5. #23781936 | C2 | semidirect |
| 6. #23781931 | C2 | semidirect |
| 7. #23781841 | C2 | semidirect |
| 8. #23781840 | C2 | semidirect |
| 9. #23781781 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #473×C163 | C2 | semidirect |
| 12. #19104783 | C22 | semidirect |
| 16. #19104766 | C22 | semidirect |
| 19. #19104763 | C22 | semidirect |
| 27. C2×#14579686 | C22 | semidirect |
| 31. #19104743 | C22 | semidirect |
| 32. #19104741 | C22 | semidirect |
| 33. #19104724 | C22 | semidirect |
| 34. #19104670 | C22 | semidirect |
| 36. #19104661 | C22 | semidirect |
| 37. #19104661 | C22 | semidirect |
| 38. #19104651 | C22 | semidirect |
| 39. C8×Dic163 | C22 | semidirect |
| 41. C2×Q16×C163 | C22 | semidirect |
| 43. #108×C163 | C22 | semidirect |
| 44. #101×C163 | C22 | semidirect |
| 149. C163 | #3290 | semidirect |
| 155. #473 | D163 | semidirect |
| 178. C2×Q16 | C2×D163 | semidirect |
| 188. #108 | C2×D163 | semidirect |
| 192. #101 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782478 | 2 |
| #23782474 | 2 |
| #23782470 | 2 |
| #23782050 | 2 |
| #23781936 | 2 |
| #23781931 | 2 |
| #23781841 | 2 |
| #23781840 | 2 |
| #23781781 | 2 |
| #23781780 | 2 |
| #473×C163 | 2 |
| #3290 | 163 |