Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
286 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 286 conjugacy classes of subgroups — too many to draw. Only its 73 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. #23781525 | C2 | semidirect |
| 3. #23781403 | C2 | semidirect |
| 4. #23781400 | C2 | semidirect |
| 5. #407×C163 | C2 | semidirect |
| 6. C2×#14579699 | C4 | semidirect |
| 8. #19104714 | C4 | semidirect |
| 10. #19104709 | C4 | semidirect |
| 15. #19104694 | C4 | semidirect |
| 117. C163 | #1513 | semidirect |
| 120. #407 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782176 | 2 |
| #23781525 | 2 |
| #23781403 | 2 |
| #23781400 | 2 |
| #407×C163 | 2 |
| #1513 | 163 |