Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
456 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 177 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. C2×#19104743 | C2 | semidirect |
| 3. #23781786 | C2 | semidirect |
| 4. #23781781 | C2 | semidirect |
| 5. #23781681 | C2 | semidirect |
| 6. #23781623 | C2 | semidirect |
| 7. #430×C163 | C2 | semidirect |
| 9. #19104768 | C4 | semidirect |
| 10. #19104763 | C4 | semidirect |
| 14. #19104743 | C22 | semidirect |
| 15. #19104743 | C22 | semidirect |
| 20. #19104661 | C22 | semidirect |
| 21. #19104645 | C22 | semidirect |
| 22. C8×Dic163 | C22 | semidirect |
| 25. #108×C163 | C22 | semidirect |
| 89. C163 | #2955 | semidirect |
| 95. #430 | D163 | semidirect |
| 112. #108 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782465 | 2 |
| C2×#19104743 | 2 |
| #23781786 | 2 |
| #23781781 | 2 |
| #23781681 | 2 |
| #23781623 | 2 |
| #430×C163 | 2 |
| #2955 | 163 |