Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
470 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 470 conjugacy classes of subgroups — too many to draw. Only its 113 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. #23762158 | C2 | semidirect |
| 4. #23762085 | C2 | semidirect |
| 6. #23761687 | C2 | semidirect |
| 7. C79×#1997 | C2 | semidirect |
| 146. #1997 | D79 | semidirect |
| 152. C79 | #9812 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098911 | 2 |
| #23764240 | 2 |
| #23762158 | 2 |
| #23762085 | 2 |
| #23762069 | 2 |
| #23761687 | 2 |
| C79×#1997 | 2 |
| #9812 | 79 |