Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
354 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 4. #23761427 | C2 | semidirect |
| 5. #23761406 | C2 | semidirect |
| 6. #23761344 | C2 | semidirect |
| 7. C79×#2769 | C2 | semidirect |
| 171. #2769 | D79 | semidirect |
| 178. C79 | #12147 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764629 | 2 |
| #23762436 | 2 |
| #23762402 | 2 |
| #23761427 | 2 |
| #23761406 | 2 |
| #23761344 | 2 |
| C79×#2769 | 2 |
| #12147 | 79 |