Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
418 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23762183 | C2 | semidirect |
| 5. #23761300 | C2 | semidirect |
| 6. #23761298 | C2 | semidirect |
| 7. C79×#1573 | C2 | semidirect |
| 192. #1573 | D79 | semidirect |
| 196. C79 | #8864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772428 | 2 |
| #23764197 | 2 |
| #23762183 | 2 |
| #23761720 | 2 |
| #23761300 | 2 |
| #23761298 | 2 |
| C79×#1573 | 2 |
| #8864 | 79 |