Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
922 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 922 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23762093 | C2 | semidirect |
| 3. #23762010 | C2 | semidirect |
| 4. #23761744 | C2 | semidirect |
| 5. C79×#1985 | C2 | semidirect |
| 152. #1985 | D79 | semidirect |
| 156. C79 | #8459 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777171 | 2 |
| #23762093 | 2 |
| #23762010 | 2 |
| #23761744 | 2 |
| C79×#1985 | 2 |
| #8459 | 79 |