Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C22×#14579686 | C2 | semidirect |
| 3. #23782139 | C2 | semidirect |
| 4. #23781877 | C2 | semidirect |
| 5. #23781867 | C2 | semidirect |
| 6. #23781692 | C2 | semidirect |
| 7. #23781674 | C2 | semidirect |
| 8. #23781661 | C2 | semidirect |
| 9. #536×C163 | C2 | semidirect |
| 22. C4⋊(C163⋊C8) | C22 | semidirect |
| 23. #19104659 | C22 | semidirect |
| 24. #19104659 | C22 | semidirect |
| 25. #19104656 | C22 | semidirect |
| 28. C4⋊Q8×C163 | C22 | semidirect |
| 29. #124×C163 | C22 | semidirect |
| 116. C163 | #3042 | semidirect |
| 120. #536 | D163 | semidirect |
| 137. C4⋊Q8 | C2×D163 | semidirect |
| 138. #124 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| C22×#14579686 | 2 |
| #23782139 | 2 |
| #23781877 | 2 |
| #23781867 | 2 |
| #23781692 | 2 |
| #23781674 | 2 |
| #23781661 | 2 |
| #536×C163 | 2 |
| #3042 | 163 |