Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 476 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. #23782468 | C2 | semidirect |
| 2. #23782467 | C2 | semidirect |
| 3. #23782040 | C2 | semidirect |
| 4. #23781935 | C2 | semidirect |
| 5. #23781933 | C2 | semidirect |
| 6. #23781932 | C2 | semidirect |
| 7. #23781833 | C2 | semidirect |
| 8. #23781831 | C2 | semidirect |
| 9. #23781782 | C2 | semidirect |
| 10. #23781780 | C2 | semidirect |
| 11. #576×C163 | C2 | semidirect |
| 12. #19104781 | C22 | semidirect |
| 15. #19104761 | C22 | semidirect |
| 17. #19104760 | C22 | semidirect |
| 18. #19104760 | C22 | semidirect |
| 22. C2×D1304 | C22 | semidirect |
| 24. C2×#14579684 | C22 | semidirect |
| 26. #19104742 | C22 | semidirect |
| 27. #19104741 | C22 | semidirect |
| 28. #19104731 | C22 | semidirect |
| 29. #19104671 | C22 | semidirect |
| 30. #19104670 | C22 | semidirect |
| 31. #19104662 | C22 | semidirect |
| 32. #19104662 | C22 | semidirect |
| 33. #19104661 | C22 | semidirect |
| 34. #19104652 | C22 | semidirect |
| 35. #19104651 | C22 | semidirect |
| 36. C8×Dic163 | C22 | semidirect |
| 37. H(5,𝔽2)×C163 | C22 | semidirect |
| 39. AGL(1,ℤ/8)×C163 | C22 | semidirect |
| 43. C2×D8×C163 | C22 | semidirect |
| 44. #131×C163 | C22 | semidirect |
| 53. #14579689 | D4 | semidirect |
| 55. #14579687 | D4 | semidirect |
| 58. #14579686 | D4 | semidirect |
| 66. #14579684 | D4 | semidirect |
| 83. Q16×C163 | D4 | semidirect |
| 85. SD16×C163 | D4 | semidirect |
| 89. D8×C163 | D4 | semidirect |
| 153. C163 | #3292 | semidirect |
| 157. #576 | D163 | semidirect |
| 167. H(5,𝔽2) | C2×D163 | semidirect |
| 175. AGL(1,ℤ/8) | C2×D163 | semidirect |
| 186. C2×D8 | C2×D163 | semidirect |
| 189. #131 | C2×D163 | semidirect |
| 216. Q16 | C22⋊D163 | semidirect |
| 223. SD16 | C22⋊D163 | semidirect |
| 235. D8 | C22⋊D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782468 | 2 |
| #23782467 | 2 |
| #23782040 | 2 |
| #23781935 | 2 |
| #23781933 | 2 |
| #23781932 | 2 |
| #23781833 | 2 |
| #23781831 | 2 |
| #23781782 | 2 |
| #23781780 | 2 |
| #576×C163 | 2 |
| #3292 | 163 |