Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
492 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 81 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. #23769279 | C2 | semidirect |
| 4. #23762026 | C2 | semidirect |
| 6. #23761848 | C2 | semidirect |
| 7. C79×#1288 | C2 | semidirect |
| 196. #1288 | D79 | semidirect |
| 197. C79 | #10021 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773801 | 2 |
| #23773523 | 2 |
| #23769279 | 2 |
| #23762026 | 2 |
| #23761946 | 2 |
| #23761848 | 2 |
| C79×#1288 | 2 |
| #10021 | 79 |