Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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. #23782016 | C2 | semidirect |
| 3. #23781961 | C2 | semidirect |
| 5. #23781412 | C2 | semidirect |
| 6. #23781397 | C2 | semidirect |
| 90. C163 | #1637 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic326 | 2 |
| #23782016 | 2 |
| #23781961 | 2 |
| #23781955 | 2 |
| #23781412 | 2 |
| #23781397 | 2 |
| D4⋊C8×C163 | 2 |
| #1637 | 163 |