Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1540 conjugacy classes of subgroups; only the 805 normal subgroups are shown.
This group has 1540 conjugacy classes of subgroups — too many to draw. Only its 805 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. #23782147 | C2 | semidirect |
| 3. #23782143 | C2 | semidirect |
| 4. #23782139 | C2 | semidirect |
| 5. C4×#14579700 | C2 | semidirect |
| 6. #117×D163 | C2 | semidirect |
| 7. #519×C163 | C2 | semidirect |
| 8. C2×#14579700 | C4 | semidirect |
| 13. Q8×Dic163 | C22 | semidirect |
| 14. C4×D652 | C22 | semidirect |
| 15. #19104697 | C22 | semidirect |
| 17. #19104693 | C22 | semidirect |
| 18. #19104692 | C22 | semidirect |
| 20. C4⋊C4×D163 | C22 | semidirect |
| 22. C42×D163 | C22 | semidirect |
| 24. C4×Q8×C163 | C22 | semidirect |
| 27. #14579700 | C2×C4 | semidirect |
| 28. #14579700 | C2×C4 | semidirect |
| 29. C2×D652 | C2×C4 | semidirect |
| 32. C2×C4×D163 | C2×C4 | semidirect |
| 42. C2×Q8×C163 | C2×C4 | semidirect |
| 79. C163 | #3428 | semidirect |
| 84. #519 | D163 | semidirect |
| 95. C4×Q8 | C2×D163 | semidirect |
| 109. C2×Q8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579700 | 2 |
| #23782147 | 2 |
| #23782143 | 2 |
| #23782139 | 2 |
| C4×#14579700 | 2 |
| #117×D163 | 2 |
| #519×C163 | 2 |
| #3428 | 163 |