Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1886 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 1886 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×#19098287 | C2 | semidirect |
| 2. #23761328 | C2 | direct (N × H) |
| 6. #19098287 | C22 | semidirect |
| 24. C25×C79 | C8 | semidirect |
| 74. C24×C79 | C2×C8 | semidirect |
| 200. C2×C79 | #1316 | semidirect |
| 206. C79 | C2×#1316 | semidirect |
| 224. C25 | C79⋊C8 | semidirect |
| 275. C24 | C2×C79⋊C8 | semidirect |
| 402. C2 | #23761328 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098287 | 2 |
| #23761328 | 2 |
| C2×#379×C79 | 2 |
| C2×#1316 | 79 |