Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
786 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 786 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. #23767044 | C2 | semidirect |
| 4. #23763334 | C2 | semidirect |
| 5. #23761971 | C2 | semidirect |
| 6. #23761248 | C2 | semidirect |
| 141. C22⋊C4×C79 | SD16 | semidirect |
| 239. C79 | #9949 | semidirect |
| 373. 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×#19098701 | 2 |
| #23767044 | 2 |
| #23763334 | 2 |
| #23761971 | 2 |
| #23761248 | 2 |
| C79×#1964 | 2 |
| #9949 | 79 |