Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 3. #23782063 | C2 | semidirect |
| 4. #23782004 | C2 | semidirect |
| 5. #23781994 | C2 | semidirect |
| 6. #23781960 | C2 | semidirect |
| 7. #23781950 | C2 | semidirect |
| 8. #23781920 | C2 | semidirect |
| 10. #23781706 | C2 | semidirect |
| 11. C4×Q16×C163 | C2 | semidirect |
| 116. C163 | #3356 | semidirect |
| 126. C4×Q16 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782388 | 2 |
| #23782375 | 2 |
| #23782063 | 2 |
| #23782004 | 2 |
| #23781994 | 2 |
| #23781960 | 2 |
| #23781950 | 2 |
| #23781920 | 2 |
| #23781744 | 2 |
| #23781706 | 2 |
| C4×Q16×C163 | 2 |
| #3356 | 163 |