Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
540 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 1. #23773801 | C2 | semidirect |
| 3. #23769271 | C2 | semidirect |
| 4. #23762026 | C2 | semidirect |
| 5. #23761946 | C2 | semidirect |
| 6. #23761844 | C2 | semidirect |
| 7. C79×#1288 | C2 | semidirect |
| 209. #1288 | D79 | semidirect |
| 210. C79 | #10019 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773801 | 2 |
| #23773492 | 2 |
| #23769271 | 2 |
| #23762026 | 2 |
| #23761946 | 2 |
| #23761844 | 2 |
| C79×#1288 | 2 |
| #10019 | 79 |