Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23781666 | C2 | semidirect |
| 3. C2×#19104657 | C2 | semidirect |
| 4. C2×#19104651 | C2 | semidirect |
| 5. #23781433 | C2 | semidirect |
| 6. #23781430 | C2 | semidirect |
| 7. C2×#131×C163 | C2 | semidirect |
| 10. #19104760 | C4 | semidirect |
| 123. C163 | #1907 | semidirect |
| 126. C2×#131 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104760 | 2 |
| #23781666 | 2 |
| C2×#19104657 | 2 |
| C2×#19104651 | 2 |
| #23781433 | 2 |
| #23781430 | 2 |
| C2×#131×C163 | 2 |
| #1907 | 163 |