Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
864 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 173 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×#19104718 | C2 | semidirect |
| 3. #23781585 | C2 | semidirect |
| 4. #23781582 | C2 | semidirect |
| 5. #23781544 | C2 | semidirect |
| 6. #23781536 | C2 | semidirect |
| 7. #23781528 | C2 | semidirect |
| 8. C22×C4⋊C4×C163 | C2 | semidirect |
| 91. C2×C4×C163 | #41 | semidirect |
| 117. C163 | #2406 | semidirect |
| 121. C22×C4⋊C4 | D163 | semidirect |
| 209. C2×C4 | #14579699 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579699 | 2 |
| C2×#19104718 | 2 |
| #23781585 | 2 |
| #23781582 | 2 |
| #23781544 | 2 |
| #23781536 | 2 |
| #23781528 | 2 |
| C22×C4⋊C4×C163 | 2 |
| #2406 | 163 |