Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 3. #23781969 | C2 | semidirect |
| 4. #23781872 | C2 | semidirect |
| 6. #23781770 | C2 | semidirect |
| 7. C4×#14579689 | C2 | semidirect |
| 95. C163 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782142 | 2 |
| #23782003 | 2 |
| #23781969 | 2 |
| #23781872 | 2 |
| #23781820 | 2 |
| #23781770 | 2 |
| C4×#14579689 | 2 |
| #23781726 | 2 |
| #541×C163 | 2 |
| #3127 | 163 |