Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
374 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 374 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 |
|---|---|---|
| 3. #23781537 | C2 | semidirect |
| 4. #23781432 | C2 | semidirect |
| 11. #19104650 | C4 | semidirect |
| 29. C22⋊Dic163 | C2×C4 | semidirect |
| 64. C23×C163 | C4⋊C4 | semidirect |
| 80. C2×C4×C163 | C4⋊C4 | semidirect |
| 112. C163 | #1867 | semidirect |
| 166. C23 | Dic163⋊C4 | semidirect |
| 193. C2×C4 | Dic163⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104650 | 2 |
| #23781545 | 2 |
| #23781537 | 2 |
| #23781432 | 2 |
| #518×C163 | 2 |
| #1867 | 163 |