Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
364 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23782220 | C2 | semidirect |
| 3. #23782074 | C2 | semidirect |
| 4. #23782033 | C2 | semidirect |
| 5. #23782024 | C2 | semidirect |
| 6. #23781920 | C2 | semidirect |
| 8. Q16×Dic163 | C2 | semidirect |
| 9. SD16×Dic163 | C2 | semidirect |
| 10. #23781617 | C2 | semidirect |
| 11. #497×C163 | C2 | semidirect |
| 129. C163 | #3172 | semidirect |
| 134. #497 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| #23782194 | 2 |
| #23782074 | 2 |
| #23782033 | 2 |
| #23782024 | 2 |
| #23781920 | 2 |
| #23781908 | 2 |
| Q16×Dic163 | 2 |
| SD16×Dic163 | 2 |
| #23781617 | 2 |
| #497×C163 | 2 |
| #3172 | 163 |