Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 173 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. #23781572 | C2 | semidirect |
| 3. #23781556 | C2 | semidirect |
| 4. #23781554 | C2 | semidirect |
| 6. #23781539 | C2 | semidirect |
| 7. #23781536 | C2 | semidirect |
| 8. #23781529 | C2 | semidirect |
| 9. #391×C163 | C2 | semidirect |
| 12. #19104724 | C4 | semidirect |
| 48. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 49. (C2×D163)⋊C4 | C2×C4 | semidirect |
| 51. C4×Dic163 | C2×C4 | semidirect |
| 54. C2×Q8×C163 | C2×C4 | semidirect |
| 123. C163 | #2379 | semidirect |
| 127. #391 | D163 | semidirect |
| 159. C2×Q8 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104724 | 2 |
| #23781572 | 2 |
| #23781556 | 2 |
| #23781554 | 2 |
| #23781543 | 2 |
| #23781539 | 2 |
| #23781536 | 2 |
| #23781529 | 2 |
| #391×C163 | 2 |
| #2379 | 163 |