Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
238 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 238 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23781715 | C2 | semidirect |
| 3. #23781510 | C2 | semidirect |
| 4. #23781403 | C2 | semidirect |
| 5. #23781401 | C2 | semidirect |
| 9. #19104726 | C4 | semidirect |
| 10. #19104722 | C4 | semidirect |
| 13. #19104700 | C4 | semidirect |
| 15. D4×Dic163 | C4 | semidirect |
| 108. C163 | #1500 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782196 | 2 |
| #23781715 | 2 |
| #23781510 | 2 |
| #23781403 | 2 |
| #23781401 | 2 |
| #23781399 | 2 |
| #327×C163 | 2 |
| #1500 | 163 |