Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1102 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1102 conjugacy classes of subgroups — too many to draw. Only its 139 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. #23762114 | C2 | semidirect |
| 2. #23762024 | C2 | semidirect |
| 3. #23761734 | C2 | semidirect |
| 5. #19098620 | C22 | semidirect |
| 211. C79 | #8522 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23762114 | 2 |
| #23762024 | 2 |
| #23761734 | 2 |
| C2×#535×C79 | 2 |
| #8522 | 79 |