Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1078 conjugacy classes of subgroups; only the 219 normal subgroups are shown.
This group has 1078 conjugacy classes of subgroups — too many to draw. Only its 219 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. C2×#19098932 | C2 | semidirect |
| 4. #23764552 | C2 | semidirect |
| 5. #23764369 | C2 | semidirect |
| 128. C22×C79 | #491 | semidirect |
| 155. C79 | #25912 | semidirect |
| 276. C22 | #19098932 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579153 | 2 |
| C2×#19098932 | 2 |
| #23771752 | 2 |
| #23764552 | 2 |
| #23764369 | 2 |
| #23763705 | 2 |
| C79×#1749 | 2 |
| #25912 | 79 |