Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
454 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 454 conjugacy classes of subgroups — too many to draw. Only its 125 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. #23782473 | C2 | semidirect |
| 2. #23782467 | C2 | semidirect |
| 3. #23782050 | C2 | semidirect |
| 4. #23781937 | C2 | semidirect |
| 5. #23781935 | C2 | semidirect |
| 6. #23781930 | C2 | semidirect |
| 7. #23781841 | C2 | semidirect |
| 8. #23781838 | C2 | semidirect |
| 9. #23781782 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #578×C163 | C2 | semidirect |
| 18. #19104760 | C22 | semidirect |
| 23. C2×#14579686 | C22 | semidirect |
| 26. #19104742 | C22 | semidirect |
| 28. #19104724 | C22 | semidirect |
| 29. #19104671 | C22 | semidirect |
| 30. #19104670 | C22 | semidirect |
| 31. #19104662 | C22 | semidirect |
| 32. #19104662 | C22 | semidirect |
| 34. #19104654 | C22 | semidirect |
| 35. #19104651 | C22 | semidirect |
| 36. C8×Dic163 | C22 | semidirect |
| 37. 2−1+4×C163 | C22 | semidirect |
| 39. #137×C163 | C22 | semidirect |
| 43. C2×Q16×C163 | C22 | semidirect |
| 44. #131×C163 | C22 | semidirect |
| 149. C163 | #3290 | semidirect |
| 151. #578 | D163 | semidirect |
| 162. 2−1+4 | C2×D163 | semidirect |
| 167. #137 | C2×D163 | semidirect |
| 178. C2×Q16 | C2×D163 | semidirect |
| 185. #131 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782473 | 2 |
| #23782467 | 2 |
| #23782050 | 2 |
| #23781937 | 2 |
| #23781935 | 2 |
| #23781930 | 2 |
| #23781841 | 2 |
| #23781838 | 2 |
| #23781782 | 2 |
| #23781780 | 2 |
| #578×C163 | 2 |
| #3290 | 163 |