Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#19104767 | C2 | semidirect |
| 2. C2×#19104762 | C2 | semidirect |
| 3. #23782216 | C2 | semidirect |
| 4. #124×D163 | C2 | semidirect |
| 5. #23782057 | C2 | semidirect |
| 6. #23782055 | C2 | semidirect |
| 7. #23782054 | C2 | semidirect |
| 8. #23782050 | C2 | semidirect |
| 9. #23782046 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #497×C163 | C2 | semidirect |
| 17. C2×#14579689 | C22 | semidirect |
| 18. C2×#14579688 | C22 | semidirect |
| 20. C2×#14579686 | C22 | semidirect |
| 24. #19104732 | C22 | semidirect |
| 26. #19104724 | C22 | semidirect |
| 34. #19104646 | C22 | semidirect |
| 35. C8×Dic163 | C22 | semidirect |
| 36. C2×Q16×C163 | C22 | semidirect |
| 38. C4⋊Q8×C163 | C22 | semidirect |
| 40. #97×C163 | C22 | semidirect |
| 63. #14579682 | D4 | semidirect |
| 134. C163 | #3153 | semidirect |
| 141. #497 | D163 | semidirect |
| 153. C2×Q16 | C2×D163 | semidirect |
| 161. C4⋊Q8 | C2×D163 | semidirect |
| 174. #97 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104767 | 2 |
| C2×#19104762 | 2 |
| #23782216 | 2 |
| #124×D163 | 2 |
| #23782057 | 2 |
| #23782055 | 2 |
| #23782054 | 2 |
| #23782050 | 2 |
| #23782046 | 2 |
| #23781617 | 2 |
| #497×C163 | 2 |
| #3153 | 163 |