Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
346 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23782282 | C2 | semidirect |
| 2. #23781953 | C2 | semidirect |
| 3. #23781949 | C2 | semidirect |
| 4. #23781923 | C2 | semidirect |
| 5. #23781892 | C2 | semidirect |
| 6. #23781886 | C2 | semidirect |
| 7. #23781878 | C2 | semidirect |
| 8. #23781693 | C2 | semidirect |
| 103. C163 | #3263 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782282 | 2 |
| #23781953 | 2 |
| #23781949 | 2 |
| #23781923 | 2 |
| #23781892 | 2 |
| #23781886 | 2 |
| #23781878 | 2 |
| #23781693 | 2 |
| #469×C163 | 2 |
| #3263 | 163 |