Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
236 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 236 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 2. #23782001 | C2 | semidirect |
| 4. #23781403 | C2 | semidirect |
| 84. C163 | #1614 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782291 | 2 |
| #23782001 | 2 |
| #23781601 | 2 |
| #23781403 | 2 |
| #323×C163 | 2 |
| #1614 | 163 |