Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
702 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 702 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
| 2. C2×#19098360 | C2 | semidirect |
| 3. #23763324 | C2 | semidirect |
| 4. #23761527 | C2 | semidirect |
| 36. #14579080 | D4 | semidirect |
| 210. C22×C79 | #355 | semidirect |
| 238. C79 | #13092 | semidirect |
| 443. C22 | #19098360 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14579080 | 2 |
| C2×#19098360 | 2 |
| #23763324 | 2 |
| #23761527 | 2 |
| C79×#2436 | 2 |
| #13092 | 79 |