Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
454 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 454 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. #23773952 | C2 | semidirect |
| 4. #23761872 | C2 | semidirect |
| 6. #23761757 | C2 | semidirect |
| 7. C79×#1291 | C2 | semidirect |
| 188. #1291 | D79 | semidirect |
| 189. C79 | #10126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774592 | 2 |
| #23774413 | 2 |
| #23773952 | 2 |
| #23761872 | 2 |
| #23761818 | 2 |
| #23761757 | 2 |
| C79×#1291 | 2 |
| #10126 | 79 |