Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23762163 | C2 | semidirect |
| 4. #23761256 | C2 | semidirect |
| 5. C4×#106×C79 | C2 | semidirect |
| 7. #19098693 | C4 | semidirect |
| 8. C8×Dic158 | C4 | semidirect |
| 9. #19098642 | C4 | semidirect |
| 11. C8×D316 | C4 | semidirect |
| 154. C4×#106 | D79 | semidirect |
| 158. C79 | #8696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772375 | 2 |
| #23762163 | 2 |
| #23761923 | 2 |
| #23761256 | 2 |
| C4×#106×C79 | 2 |
| #8696 | 79 |