Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#19104662 | C2 | semidirect |
| 3. C2×#19104661 | C2 | semidirect |
| 4. #23781664 | C2 | semidirect |
| 5. C2×#19104653 | C2 | semidirect |
| 6. #23781570 | C2 | semidirect |
| 7. #417×C163 | C2 | semidirect |
| 11. #19104782 | C4 | semidirect |
| 154. C163 | #1793 | semidirect |
| 160. #417 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| C2×#19104662 | 2 |
| C2×#19104661 | 2 |
| #23781664 | 2 |
| C2×#19104653 | 2 |
| #23781570 | 2 |
| #417×C163 | 2 |
| #1793 | 163 |