Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
536 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 536 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23763480 | C2 | semidirect |
| 4. #23761764 | C2 | semidirect |
| 6. #23761288 | C2 | semidirect |
| 7. C2×#483×C79 | C2 | semidirect |
| 196. C2×#483 | D79 | semidirect |
| 201. C79 | #9993 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774202 | 2 |
| C2×#19098881 | 2 |
| #23763480 | 2 |
| #23761764 | 2 |
| #23761759 | 2 |
| #23761288 | 2 |
| C2×#483×C79 | 2 |
| #9993 | 79 |