Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
412 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 129 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. #23782220 | C2 | semidirect |
| 3. #23782061 | C2 | semidirect |
| 4. #23782039 | C2 | semidirect |
| 5. #23782012 | C2 | semidirect |
| 6. #23781897 | C2 | semidirect |
| 7. #23781750 | C2 | semidirect |
| 8. C4×C8×D163 | C2 | semidirect |
| 9. #487×C163 | C2 | semidirect |
| 81. C4×D163 | SD16 | semidirect |
| 82. C163⋊C8 | #41 | semidirect |
| 112. C163 | #3167 | semidirect |
| 118. #487 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782220 | 2 |
| #23782216 | 2 |
| #23782061 | 2 |
| #23782039 | 2 |
| #23782012 | 2 |
| #23781897 | 2 |
| #23781750 | 2 |
| C4×C8×D163 | 2 |
| #487×C163 | 2 |
| #3167 | 163 |