Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23782044 | C2 | semidirect |
| 4. #23781417 | C2 | semidirect |
| 5. #23781411 | C2 | semidirect |
| 6. #23781410 | C2 | semidirect |
| 53. D4×C163 | Q16 | semidirect |
| 78. C163 | #1669 | semidirect |
| 127. D4 | #14579689 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782044 | 2 |
| #23781945 | 2 |
| D4×C163⋊C8 | 2 |
| #23781417 | 2 |
| #23781411 | 2 |
| #23781410 | 2 |
| #474×C163 | 2 |
| #1669 | 163 |