Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 304 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 |
|---|---|---|
| 1. #23762189 | C2 | semidirect |
| 5. #23761692 | C2 | semidirect |
| 6. #23761290 | C2 | semidirect |
| 7. C79×#1278 | C2 | semidirect |
| 150. #1278 | D79 | semidirect |
| 151. C79 | #9588 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23762189 | 2 |
| #23762060 | 2 |
| #23761852 | 2 |
| #23761818 | 2 |
| #23761692 | 2 |
| #23761290 | 2 |
| C79×#1278 | 2 |
| #9588 | 79 |