Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
354 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 89 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. #23763574 | C2 | semidirect |
| 5. #23761298 | C2 | semidirect |
| 6. #23761290 | C2 | semidirect |
| 7. C79×#1569 | C2 | semidirect |
| 171. #1569 | D79 | semidirect |
| 176. C79 | #8916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772572 | 2 |
| #23763574 | 2 |
| #23761989 | 2 |
| #23761863 | 2 |
| #23761298 | 2 |
| #23761290 | 2 |
| C79×#1569 | 2 |
| #8916 | 79 |