Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
840 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 155 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. #23774610 | C2 | semidirect |
| 3. #23762733 | C2 | semidirect |
| 5. #23762014 | C2 | semidirect |
| 162. C79 | #19058 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777814 | 2 |
| #23774610 | 2 |
| #23762733 | 2 |
| #23762035 | 2 |
| #23762014 | 2 |
| C79×#3135 | 2 |
| #19058 | 79 |