Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
556 conjugacy classes of subgroups; only the 373 normal subgroups are shown.
This group has 556 conjugacy classes of subgroups — too many to draw. Only its 373 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. #23781623 | C2 | semidirect |
| 4. #23781620 | C2 | semidirect |
| 5. M16×Dic163 | C2 | semidirect |
| 6. C2×#19104645 | C2 | semidirect |
| 8. #19104742 | C4 | semidirect |
| 21. #131×C163 | C4 | semidirect |
| 25. #14579683 | C2×C4 | semidirect |
| 26. C2×C163⋊C8 | C2×C4 | semidirect |
| 39. M16×C163 | C2×C4 | semidirect |
| 40. C2×C8×C163 | C2×C4 | semidirect |
| 68. C163 | #2875 | semidirect |
| 79. #131 | Dic163 | semidirect |
| 100. M16 | C2×Dic163 | semidirect |
| 104. C2×C8 | C2×Dic163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104742 | 2 |
| #41×Dic163 | 2 |
| #23781623 | 2 |
| #23781620 | 2 |
| M16×Dic163 | 2 |
| C2×#19104645 | 2 |
| C2×#131×C163 | 2 |
| #2875 | 163 |