Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
610 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 161 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×#19104691 | C2 | semidirect |
| 3. C22×Dic163⋊C4 | C2 | semidirect |
| 4. #23781596 | C2 | semidirect |
| 5. #23781588 | C2 | semidirect |
| 6. #23781561 | C2 | semidirect |
| 7. #23781553 | C2 | semidirect |
| 9. #23781540 | C2 | semidirect |
| 10. #23781528 | C2 | semidirect |
| 147. C163 | #2413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104716 | 2 |
| C2×#19104691 | 2 |
| C22×Dic163⋊C4 | 2 |
| #23781596 | 2 |
| #23781588 | 2 |
| #23781561 | 2 |
| #23781553 | 2 |
| #23781545 | 2 |
| #23781540 | 2 |
| #23781528 | 2 |
| C2×#123×C163 | 2 |
| #2413 | 163 |