Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
270 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 55 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. #23781637 | C2 | semidirect |
| 3. #23781458 | C2 | semidirect |
| 4. #23781457 | C2 | semidirect |
| 5. #353×C163 | C2 | semidirect |
| 7. C2×D4×D163 | C4 | semidirect |
| 9. #19104723 | C4 | semidirect |
| 10. #19104722 | C4 | semidirect |
| 13. #19104692 | C4 | semidirect |
| 15. #19104650 | C22 | semidirect |
| 18. #99×C163 | C22 | semidirect |
| 89. C163 | #2128 | semidirect |
| 95. #353 | D163 | semidirect |
| 108. #99 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782228 | 2 |
| #23781637 | 2 |
| #23781458 | 2 |
| #23781457 | 2 |
| #353×C163 | 2 |
| #2128 | 163 |