Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
456 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 3. C2×#19098378 | C2 | semidirect |
| 4. #23764315 | C2 | semidirect |
| 5. #23761513 | C2 | semidirect |
| 6. #23761486 | C2 | semidirect |
| 10. #19099003 | C4 | semidirect |
| 174. C79 | #13031 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099003 | 2 |
| #23765149 | 2 |
| C2×#19098378 | 2 |
| #23764315 | 2 |
| #23761513 | 2 |
| #23761486 | 2 |
| C79×#2957 | 2 |
| #13031 | 79 |