Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
400 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 133 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. #23782222 | C2 | semidirect |
| 2. #23782024 | C2 | semidirect |
| 3. #23782019 | C2 | semidirect |
| 4. #23781674 | C2 | semidirect |
| 6. C4×#14579683 | C2 | semidirect |
| 9. #19104735 | C22 | semidirect |
| 10. #19104727 | C22 | semidirect |
| 14. #19104659 | C22 | semidirect |
| 16. #19104646 | C22 | semidirect |
| 17. C4×C163⋊C8 | C22 | semidirect |
| 83. C163 | #3140 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782222 | 2 |
| #23782024 | 2 |
| #23782019 | 2 |
| #23781674 | 2 |
| #23781670 | 2 |
| C4×#14579683 | 2 |
| C2×#124×C163 | 2 |
| #3140 | 163 |