Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
1088 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1088 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. C2×#19104724 | C2 | semidirect |
| 3. #23781582 | C2 | semidirect |
| 4. #23781566 | C2 | semidirect |
| 5. #23781520 | C2 | semidirect |
| 6. C4×C22⋊Dic163 | C2 | semidirect |
| 7. C2×C22⋊Q8×C163 | C2 | semidirect |
| 15. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 16. C2×(C2×D163)⋊C4 | C22 | semidirect |
| 17. C2×C4×Dic163 | C22 | semidirect |
| 18. C163⋊#95 | C22 | semidirect |
| 19. C22×Q8×C163 | C22 | semidirect |
| 22. C2×C4⋊C4×C163 | C22 | semidirect |
| 23. C2×C4⋊C4×C163 | C22 | semidirect |
| 85. C22×C163 | #124 | semidirect |
| 107. C163 | #2435 | semidirect |
| 111. C2×C22⋊Q8 | D163 | semidirect |
| 117. C22×Q8 | C2×D163 | semidirect |
| 125. C2×C4⋊C4 | C2×D163 | semidirect |
| 126. C2×C4⋊C4 | C2×D163 | semidirect |
| 199. C22 | #19104724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D652 | 2 |
| C2×#19104724 | 2 |
| #23781582 | 2 |
| #23781566 | 2 |
| #23781520 | 2 |
| C4×C22⋊Dic163 | 2 |
| C2×C22⋊Q8×C163 | 2 |
| #2435 | 163 |