Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
296 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 296 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 |
|---|---|---|
| 4. #23781432 | C2 | semidirect |
| 5. #23781431 | C2 | semidirect |
| 6. #23781431 | C2 | semidirect |
| 7. #342×C163 | C2 | semidirect |
| 11. #19104691 | C4 | semidirect |
| 15. C22⋊C4×D163 | C4 | semidirect |
| 118. C163 | #1828 | semidirect |
| 126. #342 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782138 | 2 |
| C2×#19104649 | 2 |
| #23781432 | 2 |
| #23781431 | 2 |
| #342×C163 | 2 |
| #1828 | 163 |