Finite Group DatabasebetaFinite Group DatabasebetaOrder 20864.
370 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 123 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. #23782393 | C2 | semidirect |
| 3. #23782017 | C2 | semidirect |
| 4. #23782014 | C2 | semidirect |
| 5. #23781949 | C2 | semidirect |
| 8. #23781789 | C2 | semidirect |
| 11. #475×C163 | C2 | semidirect |
| 78. Dic326 | SD16 | semidirect |
| 118. C163 | #3359 | semidirect |
| 125. #475 | D163 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23782393 | 2 |
| #23782330 | 2 |
| #23782017 | 2 |
| #23782014 | 2 |
| #23781949 | 2 |
| #23781871 | 2 |
| #23781869 | 2 |
| #23781789 | 2 |
| C4×#14579686 | 2 |
| #23781752 | 2 |
| #475×C163 | 2 |
| #3359 | 163 |