Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
610 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 610 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23767878 | C2 | semidirect |
| 4. #23763488 | C2 | semidirect |
| 5. #23761971 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 127. C22⋊C4×C79 | SD16 | semidirect |
| 218. C79 | #9951 | semidirect |
| 338. C22⋊C4 | #11929612 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774157 | 2 |
| C2×#19098879 | 2 |
| #23767878 | 2 |
| #23763488 | 2 |
| #23761971 | 2 |
| #23761248 | 2 |
| C79×#1964 | 2 |
| #9951 | 79 |