Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
374 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782068 | C2 | semidirect |
| 3. #23781998 | C2 | semidirect |
| 4. #23781989 | C2 | semidirect |
| 5. #23781950 | C2 | semidirect |
| 6. #23781942 | C2 | semidirect |
| 7. #23781913 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. #23781743 | C2 | semidirect |
| 10. #23781708 | C2 | semidirect |
| 11. #556×C163 | C2 | semidirect |
| 85. C163⋊C8 | #41 | semidirect |
| 122. C163 | #3353 | semidirect |
| 124. #556 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782319 | 2 |
| #23782068 | 2 |
| #23781998 | 2 |
| #23781989 | 2 |
| #23781950 | 2 |
| #23781942 | 2 |
| #23781913 | 2 |
| C4×#14579686 | 2 |
| #23781743 | 2 |
| #23781708 | 2 |
| #556×C163 | 2 |
| #3353 | 163 |