Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
872 conjugacy classes of subgroups; only the 315 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 315 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. #23762038 | C2 | semidirect |
| 3. #23762002 | C2 | semidirect |
| 4. #23761995 | C2 | semidirect |
| 104. C79 | #17692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772420 | 2 |
| #23762038 | 2 |
| #23762002 | 2 |
| #23761995 | 2 |
| C79×#3504 | 2 |
| #17692 | 79 |