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×#19104782 | C2 | semidirect |
| 2. #23782463 | C2 | semidirect |
| 3. #23782236 | C2 | semidirect |
| 4. #23781846 | C2 | semidirect |
| 5. #23781836 | C2 | semidirect |
| 6. #23781682 | C2 | semidirect |
| 7. #23781681 | C2 | semidirect |
| 8. C2×#19104653 | C2 | semidirect |
| 9. #575×C163 | C2 | semidirect |
| 21. #19104766 | C22 | semidirect |
| 23. #19104761 | C22 | semidirect |
| 27. #19104733 | C22 | semidirect |
| 28. #19104722 | C22 | semidirect |
| 32. #19104662 | C22 | semidirect |
| 33. #19104661 | C22 | semidirect |
| 34. #19104653 | C22 | semidirect |
| 38. #137×C163 | C22 | semidirect |
| 40. AGL(1,ℤ/8)×C163 | C22 | semidirect |
| 185. C163 | #3020 | semidirect |
| 189. #575 | D163 | semidirect |
| 212. #137 | C2×D163 | semidirect |
| 216. AGL(1,ℤ/8) | C2×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104782 | 2 |
| #23782463 | 2 |
| #23782236 | 2 |
| #23781846 | 2 |
| #23781836 | 2 |
| #23781682 | 2 |
| #23781681 | 2 |
| C2×#19104653 | 2 |
| #575×C163 | 2 |
| #3020 | 163 |