Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
320 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 320 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. #23781689 | C2 | semidirect |
| 3. C2×#19104663 | C2 | semidirect |
| 4. #376×C163 | C2 | semidirect |
| 7. #19104735 | C4 | semidirect |
| 8. #19104732 | C4 | semidirect |
| 9. #19104723 | C4 | semidirect |
| 35. C42×C163 | D4 | semidirect |
| 71. C163 | #1963 | semidirect |
| 76. #376 | D163 | semidirect |
| 107. C42 | D652 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782215 | 2 |
| #23781689 | 2 |
| C2×#19104663 | 2 |
| #376×C163 | 2 |
| #1963 | 163 |