Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
384 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23782401 | C2 | semidirect |
| 2. D4×Dic326 | C2 | semidirect |
| 3. #23782023 | C2 | semidirect |
| 4. #23782011 | C2 | semidirect |
| 5. #23781953 | C2 | semidirect |
| 6. #23781951 | C2 | semidirect |
| 7. #23781878 | C2 | semidirect |
| 8. #23781792 | C2 | semidirect |
| 9. #23781777 | C2 | semidirect |
| 10. C4×#14579687 | C2 | semidirect |
| 124. C163 | #3373 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782401 | 2 |
| D4×Dic326 | 2 |
| #23782023 | 2 |
| #23782011 | 2 |
| #23781953 | 2 |
| #23781951 | 2 |
| #23781878 | 2 |
| #23781792 | 2 |
| #23781777 | 2 |
| C4×#14579687 | 2 |
| #459×C163 | 2 |
| #3373 | 163 |