Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
420 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. #23782015 | C2 | semidirect |
| 3. #23781993 | C2 | semidirect |
| 4. #23781950 | C2 | semidirect |
| 5. #23781896 | C2 | semidirect |
| 6. #23781867 | C2 | semidirect |
| 7. #23781804 | C2 | semidirect |
| 8. C4×#14579686 | C2 | semidirect |
| 9. D4×C163⋊C8 | C2 | semidirect |
| 10. C2×#19104659 | C2 | semidirect |
| 11. D4×Q8×C163 | C2 | semidirect |
| 94. Q8×C163 | #41 | semidirect |
| 95. D4×C163 | SD16 | semidirect |
| 128. C163 | #3298 | semidirect |
| 130. D4×Q8 | D163 | semidirect |
| 213. Q8 | #14579698 | semidirect |
| 217. D4 | #14579686 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782319 | 2 |
| #23782015 | 2 |
| #23781993 | 2 |
| #23781950 | 2 |
| #23781896 | 2 |
| #23781867 | 2 |
| #23781804 | 2 |
| C4×#14579686 | 2 |
| D4×C163⋊C8 | 2 |
| C2×#19104659 | 2 |
| D4×Q8×C163 | 2 |
| #3298 | 163 |