Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#19104783 | C2 | semidirect |
| 2. #23782463 | C2 | semidirect |
| 3. #23781847 | C2 | semidirect |
| 4. #23781837 | C2 | semidirect |
| 5. #23781683 | C2 | semidirect |
| 6. C2×#19104654 | C2 | semidirect |
| 7. #536×C163 | C2 | semidirect |
| 15. #19104766 | C22 | semidirect |
| 17. #19104761 | C22 | semidirect |
| 21. #19104663 | C22 | semidirect |
| 22. #19104654 | C22 | semidirect |
| 25. C4⋊Q8×C163 | C22 | semidirect |
| 26. #124×C163 | C22 | semidirect |
| 123. C163 | #3020 | semidirect |
| 127. #536 | D163 | semidirect |
| 147. C4⋊Q8 | C2×D163 | semidirect |
| 148. #124 | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104783 | 2 |
| #23782463 | 2 |
| #23781847 | 2 |
| #23781837 | 2 |
| #23781683 | 2 |
| C2×#19104654 | 2 |
| #536×C163 | 2 |
| #3020 | 163 |