Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
702 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 107 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. C22×#14579080 | C2 | semidirect |
| 3. C2×#19098359 | C2 | semidirect |
| 4. #23761526 | C2 | semidirect |
| 5. C79×#1784 | C2 | semidirect |
| 48. #14579080 | D4 | semidirect |
| 205. C22×C79 | #355 | semidirect |
| 236. #1784 | D79 | semidirect |
| 238. C79 | #13092 | semidirect |
| 443. C22 | #19098359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579080 | 2 |
| #23767054 | 2 |
| C2×#19098359 | 2 |
| #23761526 | 2 |
| C79×#1784 | 2 |
| #13092 | 79 |