Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#19099003 | C2 | semidirect |
| 2. C2×#19098821 | C2 | semidirect |
| 3. C2×#19098373 | C2 | semidirect |
| 4. #23765119 | C2 | semidirect |
| 5. C2×#19098345 | C2 | semidirect |
| 6. #23761505 | C2 | semidirect |
| 37. C2×Dic316 | D4 | semidirect |
| 48. #14579101 | D4 | semidirect |
| 52. #14579093 | D4 | semidirect |
| 219. C79 | #13317 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099003 | 2 |
| C2×#19098821 | 2 |
| C2×#19098373 | 2 |
| #23765119 | 2 |
| C2×#19098345 | 2 |
| #23761505 | 2 |
| C79×#3054 | 2 |
| #13317 | 79 |