Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
492 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 133 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×#14579687 | C2 | semidirect |
| 2. C2×#19104743 | C2 | semidirect |
| 3. #23782241 | C2 | semidirect |
| 5. #23781910 | C2 | semidirect |
| 6. #23781893 | C2 | semidirect |
| 7. #23781701 | C2 | semidirect |
| 8. #23781675 | C2 | semidirect |
| 9. #418×C163 | C2 | semidirect |
| 16. C2×#14579682 | C22 | semidirect |
| 18. C2×C8×D163 | C22 | semidirect |
| 24. #19104715 | C22 | semidirect |
| 28. #19104668 | C22 | semidirect |
| 29. #19104666 | C22 | semidirect |
| 30. #19104660 | C22 | semidirect |
| 50. C2×C163⋊C8 | D4 | semidirect |
| 120. C163 | #3057 | semidirect |
| 130. #418 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579687 | 2 |
| C2×#19104743 | 2 |
| #23782241 | 2 |
| #23782232 | 2 |
| #23781910 | 2 |
| #23781893 | 2 |
| #23781701 | 2 |
| #23781675 | 2 |
| #418×C163 | 2 |
| #3057 | 163 |