Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
304 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 85 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. #23765172 | C2 | semidirect |
| 2. #23765158 | C2 | semidirect |
| 6. #23764188 | C2 | semidirect |
| 7. C79×#1382 | C2 | semidirect |
| 143. #1382 | D79 | semidirect |
| 144. C79 | #13468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765172 | 2 |
| #23765158 | 2 |
| #23765127 | 2 |
| C2×#19098371 | 2 |
| #23764296 | 2 |
| #23764188 | 2 |
| C79×#1382 | 2 |
| #13468 | 79 |