Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
528 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 181 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. #23782140 | C2 | semidirect |
| 3. #23782139 | C2 | semidirect |
| 4. #23781774 | C2 | semidirect |
| 5. #23781745 | C2 | semidirect |
| 6. #23781701 | C2 | semidirect |
| 7. #23781671 | C2 | semidirect |
| 8. #23781623 | C2 | semidirect |
| 9. #418×C163 | C2 | semidirect |
| 11. C2×#14579684 | C4 | semidirect |
| 17. D4×Dic163 | C22 | semidirect |
| 18. #19104697 | C22 | semidirect |
| 23. #19104668 | C22 | semidirect |
| 24. #19104666 | C22 | semidirect |
| 25. #19104657 | C22 | semidirect |
| 26. #19104645 | C22 | semidirect |
| 27. C8×Dic163 | C22 | semidirect |
| 31. #102×C163 | C22 | semidirect |
| 35. C2×D652 | C2×C4 | semidirect |
| 39. #14579684 | C2×C4 | semidirect |
| 40. #14579684 | C2×C4 | semidirect |
| 41. C2×C163⋊C8 | C2×C4 | semidirect |
| 55. C2×D4×C163 | C2×C4 | semidirect |
| 108. C163 | #2948 | semidirect |
| 117. #418 | D163 | semidirect |
| 138. #102 | C2×D163 | semidirect |
| 149. C2×D4 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579684 | 2 |
| #23782140 | 2 |
| #23782139 | 2 |
| #23781774 | 2 |
| #23781745 | 2 |
| #23781701 | 2 |
| #23781671 | 2 |
| #23781623 | 2 |
| #418×C163 | 2 |
| #2948 | 163 |