Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 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 |
|---|---|---|
| 1. C22×#14579688 | C2 | semidirect |
| 2. C2×#19104714 | C2 | semidirect |
| 4. #23781894 | C2 | direct (N × H) |
| 5. C2×#19104667 | C2 | semidirect |
| 6. C2×#19104660 | C2 | semidirect |
| 7. C2×#19104657 | C2 | semidirect |
| 8. C23×C8×C163 | C2 | semidirect |
| 13. C2×#14579688 | C22 | semidirect |
| 15. #19104714 | C22 | semidirect |
| 23. #19104667 | C22 | semidirect |
| 24. #19104660 | C22 | semidirect |
| 25. #19104657 | C22 | semidirect |
| 30. C22×C8×C163 | C22 | semidirect |
| 62. C2×C8×C163 | D4 | semidirect |
| 84. C23×C163 | SD16 | semidirect |
| 97. C8×C163 | C2×D4 | semidirect |
| 103. C22×C163 | C2×SD16 | semidirect |
| 118. C2×C163 | #465 | semidirect |
| 123. C163 | C2×#465 | semidirect |
| 126. C23×C8 | D163 | semidirect |
| 142. C22×C8 | C2×D163 | semidirect |
| 179. C2×C8 | C22⋊D163 | semidirect |
| 195. C23 | #14579688 | semidirect |
| 221. C8 | C2×C22⋊D163 | semidirect |
| 231. C22 | C2×#14579688 | semidirect |
| 243. C2 | #23781894 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579688 | 2 |
| C2×#19104714 | 2 |
| C2×#19104709 | 2 |
| #23781894 | 2 |
| C2×#19104667 | 2 |
| C2×#19104660 | 2 |
| C2×#19104657 | 2 |
| C23×C8×C163 | 2 |
| C2×#465 | 163 |