Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
920 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 920 conjugacy classes of subgroups — too many to draw. Only its 179 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. #23773952 | C2 | semidirect |
| 4. #23769350 | C2 | semidirect |
| 6. #23764380 | C2 | semidirect |
| 7. #23763617 | C2 | semidirect |
| 9. C79×#1966 | C2 | semidirect |
| 195. #1966 | D79 | semidirect |
| 198. C79 | #25691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777284 | 2 |
| #23773952 | 2 |
| #23773223 | 2 |
| #23769350 | 2 |
| #23764618 | 2 |
| #23764380 | 2 |
| #23763617 | 2 |
| #23763213 | 2 |
| C79×#1966 | 2 |
| #25691 | 79 |