Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
336 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 67 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. #23761570 | C2 | semidirect |
| 4. #23761564 | C2 | semidirect |
| 6. #19099175 | C4 | semidirect |
| 7. #19098958 | C4 | semidirect |
| 10. #19098917 | C4 | semidirect |
| 15. #19098624 | C4 | semidirect |
| 27. #14579161 | C2×C4 | semidirect |
| 29. #14579153 | C2×C4 | semidirect |
| 42. #14579072 | C2×C4 | semidirect |
| 43. C4×C79⋊C8 | C2×C4 | semidirect |
| 159. C79 | #13610 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774472 | 2 |
| #23765069 | 2 |
| #23761570 | 2 |
| #23761564 | 2 |
| C79×#2128 | 2 |
| #13610 | 79 |