Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
880 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 133 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. C2×#19104650 | C2 | semidirect |
| 2. #23781521 | C2 | semidirect |
| 5. C2×C22⋊Dic163 | C22 | semidirect |
| 7. C25×C163 | C4 | semidirect |
| 11. C22×D4×C163 | C4 | semidirect |
| 13. C23×C4×C163 | C4 | semidirect |
| 57. C23×C163 | C22⋊C4 | semidirect |
| 66. C2×C4×C163 | C22⋊C4 | semidirect |
| 82. C22×C163 | #99 | semidirect |
| 95. C163 | #1781 | semidirect |
| 100. C25 | Dic163 | semidirect |
| 104. C22×D4 | Dic163 | semidirect |
| 106. C23×C4 | Dic163 | semidirect |
| 151. C23 | C22⋊Dic163 | semidirect |
| 162. C2×C4 | C22⋊Dic163 | semidirect |
| 178. C22 | #19104650 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104650 | 2 |
| #23781521 | 2 |
| C23×D4×C163 | 2 |
| #1781 | 163 |