Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
600 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 600 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 4. #23781562 | C2 | semidirect |
| 6. #23781535 | C2 | semidirect |
| 7. #23781534 | C2 | semidirect |
| 8. #23781530 | C2 | semidirect |
| 9. #382×C163 | C2 | semidirect |
| 13. #19104692 | C4 | semidirect |
| 45. Dic163⋊C4 | C2×C4 | semidirect |
| 49. C4×Dic163 | C2×C4 | semidirect |
| 56. C42×C163 | C2×C4 | semidirect |
| 73. C4×D163 | C4⋊C4 | semidirect |
| 109. C163 | #2317 | semidirect |
| 119. #382 | D163 | semidirect |
| 166. C42 | C4×D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104693 | 2 |
| C2×#19104692 | 2 |
| C2×C4⋊C4×D163 | 2 |
| #23781562 | 2 |
| #23781539 | 2 |
| #23781535 | 2 |
| #23781534 | 2 |
| #23781530 | 2 |
| #382×C163 | 2 |
| #2317 | 163 |