Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
390 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 57 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. #23765334 | C2 | semidirect |
| 4. #23761419 | C2 | semidirect |
| 5. #23761418 | C2 | semidirect |
| 7. C79×#2188 | C2 | semidirect |
| 174. #2188 | D79 | semidirect |
| 179. C79 | #12112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774290 | 2 |
| #23765334 | 2 |
| #23764519 | 2 |
| #23761419 | 2 |
| #23761418 | 2 |
| #23761325 | 2 |
| C79×#2188 | 2 |
| #12112 | 79 |