Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
698 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 698 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 |
|---|---|---|
| 1. #23782463 | C2 | semidirect |
| 2. #23782239 | C2 | semidirect |
| 3. #23781848 | C2 | semidirect |
| 4. #23781838 | C2 | semidirect |
| 5. #23781682 | C2 | semidirect |
| 6. C2×#19104654 | C2 | semidirect |
| 7. C2×2−1+4×C163 | C2 | semidirect |
| 10. #19104765 | C22 | semidirect |
| 12. #19104760 | C22 | semidirect |
| 15. #19104733 | C22 | semidirect |
| 16. #19104724 | C22 | semidirect |
| 20. #19104662 | C22 | semidirect |
| 21. #19104654 | C22 | semidirect |
| 123. C163 | #3020 | semidirect |
| 125. C2×2−1+4 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782463 | 2 |
| #23782239 | 2 |
| #23781848 | 2 |
| #23781838 | 2 |
| #23781682 | 2 |
| C2×#19104654 | 2 |
| C2×2−1+4×C163 | 2 |
| #3020 | 163 |