Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 1. C22×#14579686 | C2 | semidirect |
| 2. C2×#19104742 | C2 | semidirect |
| 4. #23781913 | C2 | semidirect |
| 5. #23781896 | C2 | semidirect |
| 6. #23781701 | C2 | semidirect |
| 7. #23781674 | C2 | semidirect |
| 8. #23781669 | C2 | semidirect |
| 9. #536×C163 | C2 | semidirect |
| 16. C2×#14579683 | C22 | semidirect |
| 18. C22×C163⋊C8 | C22 | semidirect |
| 24. #19104668 | C22 | semidirect |
| 25. #19104666 | C22 | semidirect |
| 26. #19104659 | C22 | semidirect |
| 33. C22⋊Q8×C163 | C22 | semidirect |
| 46. C2×C163⋊C8 | D4 | semidirect |
| 120. C163 | #3057 | semidirect |
| 124. #536 | D163 | semidirect |
| 147. C22⋊Q8 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579686 | 2 |
| C2×#19104742 | 2 |
| #23782229 | 2 |
| #23781913 | 2 |
| #23781896 | 2 |
| #23781701 | 2 |
| #23781674 | 2 |
| #23781669 | 2 |
| #536×C163 | 2 |
| #3057 | 163 |