Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
168 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 51 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. #23781951 | C2 | semidirect |
| 4. #23781792 | C2 | semidirect |
| 5. #23781417 | C2 | semidirect |
| 6. #23781412 | C2 | semidirect |
| 51. C163⋊C8 | SD16 | semidirect |
| 79. C163 | #1686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782037 | 2 |
| #23781951 | 2 |
| #23781862 | 2 |
| #23781792 | 2 |
| #23781417 | 2 |
| #23781412 | 2 |
| #331×C163 | 2 |
| #1686 | 163 |