Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
602 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 602 conjugacy classes of subgroups — too many to draw. Only its 163 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. #23763517 | C2 | semidirect |
| 3. C2×#19098310 | C2 | semidirect |
| 5. C4×C4⋊C8×C79 | C2 | semidirect |
| 144. C4×C4⋊C8 | D79 | semidirect |
| 147. C79 | #9696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771757 | 2 |
| #23763517 | 2 |
| C2×#19098310 | 2 |
| C2×#19098306 | 2 |
| C4×C4⋊C8×C79 | 2 |
| #9696 | 79 |