Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 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. #23782389 | C2 | semidirect |
| 3. #23782017 | C2 | semidirect |
| 4. #23782008 | C2 | semidirect |
| 5. #23781907 | C2 | semidirect |
| 6. #23781876 | C2 | semidirect |
| 7. #23781828 | C2 | semidirect |
| 8. C4×#14579687 | C2 | semidirect |
| 9. #23781730 | C2 | semidirect |
| 10. #23781658 | C2 | semidirect |
| 11. #474×C163 | C2 | semidirect |
| 125. C163 | #3302 | semidirect |
| 131. #474 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782389 | 2 |
| #23782319 | 2 |
| #23782017 | 2 |
| #23782008 | 2 |
| #23781907 | 2 |
| #23781876 | 2 |
| #23781828 | 2 |
| C4×#14579687 | 2 |
| #23781730 | 2 |
| #23781658 | 2 |
| #474×C163 | 2 |
| #3302 | 163 |