Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
774 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 774 conjugacy classes of subgroups — too many to draw. Only its 297 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 |
|---|---|---|
| 1. C2×#19104742 | C2 | semidirect |
| 2. #23781632 | C2 | semidirect |
| 3. #23781629 | C2 | semidirect |
| 4. C2×C22⋊(C163⋊C8) | C2 | semidirect |
| 7. C2×#14579683 | C22 | semidirect |
| 8. C22×C163⋊C8 | C22 | semidirect |
| 11. C22⋊(C163⋊C8) | C22 | semidirect |
| 12. C22⋊(C163⋊C8) | C22 | semidirect |
| 76. C22×C163 | #131 | semidirect |
| 88. C163 | #2880 | semidirect |
| 165. C22 | #19104742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104742 | 2 |
| #23781632 | 2 |
| #23781629 | 2 |
| C2×C22⋊(C163⋊C8) | 2 |
| C22×#41×C163 | 2 |
| #2880 | 163 |