Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
344 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 344 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23782432 | C2 | semidirect |
| 2. #23781670 | C2 | semidirect |
| 3. #23781639 | C2 | semidirect |
| 4. #23781421 | C2 | semidirect |
| 14. #127×C163 | C4 | semidirect |
| 15. #124×C163 | C4 | semidirect |
| 23. C2×C163⋊C8 | D4 | semidirect |
| 85. C163 | #1910 | semidirect |
| 97. #127 | Dic163 | semidirect |
| 98. #124 | Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782432 | 2 |
| #23781670 | 2 |
| #23781639 | 2 |
| #23781421 | 2 |
| #535×C163 | 2 |
| #1910 | 163 |