Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
368 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782069 | C2 | semidirect |
| 3. #23782043 | C2 | semidirect |
| 4. #23782014 | C2 | semidirect |
| 7. Q16×Dic163 | C2 | semidirect |
| 8. #23781759 | C2 | semidirect |
| 9. #23781757 | C2 | semidirect |
| 77. C2×Dic163 | Q16 | semidirect |
| 114. C163 | #3170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782217 | 2 |
| #23782069 | 2 |
| #23782043 | 2 |
| #23782014 | 2 |
| #23781906 | 2 |
| #23781904 | 2 |
| Q16×Dic163 | 2 |
| #23781759 | 2 |
| #23781757 | 2 |
| C2×C8×Dic163 | 2 |
| #467×C163 | 2 |
| #3170 | 163 |