Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
746 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 746 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23762098 | C2 | semidirect |
| 4. #23762016 | C2 | semidirect |
| 5. #23762015 | C2 | semidirect |
| 7. C79×#1552 | C2 | semidirect |
| 218. #1552 | D79 | semidirect |
| 222. C79 | #8457 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777201 | 2 |
| #23764197 | 2 |
| #23762098 | 2 |
| #23762016 | 2 |
| #23762015 | 2 |
| #23761740 | 2 |
| C79×#1552 | 2 |
| #8457 | 79 |