Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
376 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 135 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. #23781975 | C2 | semidirect |
| 4. #23781971 | C2 | semidirect |
| 5. #23781959 | C2 | semidirect |
| 6. #23781949 | C2 | semidirect |
| 47. C2×Dic326 | Q8 | semidirect |
| 129. C163 | #3078 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782218 | 2 |
| C2×#19104700 | 2 |
| #23781975 | 2 |
| #23781971 | 2 |
| #23781959 | 2 |
| #23781949 | 2 |
| #23781705 | 2 |
| #23781688 | 2 |
| #23781675 | 2 |
| #23781673 | 2 |
| #428×C163 | 2 |
| #3078 | 163 |