Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 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. #23782039 | C2 | semidirect |
| 3. D4×C163⋊C8 | C2 | semidirect |
| 4. #23781415 | C2 | semidirect |
| 5. #23781411 | C2 | semidirect |
| 6. #23781408 | C2 | semidirect |
| 7. #474×C163 | C2 | semidirect |
| 52. C163⋊C8 | D8 | semidirect |
| 57. D4×C163 | SD16 | semidirect |
| 85. C163 | #1665 | semidirect |
| 88. #474 | D163 | semidirect |
| 139. D4 | #14579686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782039 | 2 |
| #23781860 | 2 |
| D4×C163⋊C8 | 2 |
| #23781415 | 2 |
| #23781411 | 2 |
| #23781408 | 2 |
| #474×C163 | 2 |
| #1665 | 163 |