Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
210 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23781713 | C2 | semidirect |
| 2. #23781691 | C2 | semidirect |
| 6. #23781421 | C2 | semidirect |
| 7. #424×C163 | C2 | semidirect |
| 89. C163 | #2098 | semidirect |
| 93. #424 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23781713 | 2 |
| #23781691 | 2 |
| #23781683 | 2 |
| #23781681 | 2 |
| #23781631 | 2 |
| #23781421 | 2 |
| #424×C163 | 2 |
| #2098 | 163 |