Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23782390 | C2 | semidirect |
| 4. #23782017 | C2 | semidirect |
| 5. #23781971 | C2 | semidirect |
| 7. #23781876 | C2 | semidirect |
| 8. #23781789 | C2 | semidirect |
| 9. #23781759 | C2 | semidirect |
| 115. C163 | #3364 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782390 | 2 |
| #23782385 | 2 |
| #23782018 | 2 |
| #23782017 | 2 |
| #23781971 | 2 |
| #23781886 | 2 |
| #23781876 | 2 |
| #23781789 | 2 |
| #23781759 | 2 |
| C4×#14579687 | 2 |
| #474×C163 | 2 |
| #3364 | 163 |