Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
126 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 126 conjugacy classes of subgroups — too many to draw. Only its 45 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. #23782062 | C2 | semidirect |
| 3. #23781488 | C2 | semidirect |
| 4. #23781487 | C2 | semidirect |
| 5. #23781485 | C2 | semidirect |
| 29. Q16×C163 | Q8 | semidirect |
| 31. D8×C163 | Q8 | semidirect |
| 60. C163 | #2230 | semidirect |
| 82. Q16 | Dic326 | semidirect |
| 84. D8 | Dic326 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782062 | 2 |
| #23781782 | 2 |
| #23781488 | 2 |
| #23781487 | 2 |
| #23781485 | 2 |
| #23781475 | 2 |
| #360×C163 | 2 |
| #2230 | 163 |