Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
848 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 848 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 |
|---|---|---|
| 2. C2×#19098359 | C2 | semidirect |
| 3. #23763801 | C2 | semidirect |
| 4. #23763794 | C2 | semidirect |
| 5. C2×#356×C79 | C2 | semidirect |
| 8. #19099279 | C4 | semidirect |
| 171. C2×#356 | D79 | semidirect |
| 175. C79 | #12776 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099279 | 2 |
| C2×#19098359 | 2 |
| #23763801 | 2 |
| #23763794 | 2 |
| C2×#356×C79 | 2 |
| #12776 | 79 |