Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23768567 | C2 | semidirect |
| 3. #23764320 | C2 | semidirect |
| 4. #23762002 | C2 | semidirect |
| 5. #23761842 | C2 | semidirect |
| 6. #23761257 | C2 | semidirect |
| 7. C79×#3234 | C2 | semidirect |
| 217. #3234 | D79 | semidirect |
| 224. C79 | #10005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773487 | 2 |
| #23768567 | 2 |
| #23764320 | 2 |
| #23762002 | 2 |
| #23761842 | 2 |
| #23761257 | 2 |
| C79×#3234 | 2 |
| #10005 | 79 |