Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
516 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 516 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 11. #19104733 | C4 | semidirect |
| 100. C163 | #2327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19104733 | 2 |
| C2×C4×Dic326 | 2 |
| #23781572 | 2 |
| #23781570 | 2 |
| #23781549 | 2 |
| #23781546 | 2 |
| #23781530 | 2 |
| #23781511 | 2 |
| C2×C4×Q8×C163 | 2 |
| #2327 | 163 |