Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
434 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 434 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 |
|---|---|---|
| 4. #23765120 | C2 | semidirect |
| 5. #23765004 | C2 | semidirect |
| 6. #23763525 | C2 | semidirect |
| 7. C2×#362×C79 | C2 | semidirect |
| 13. #19098948 | C4 | semidirect |
| 14. #19098941 | C4 | semidirect |
| 170. C2×#362 | D79 | semidirect |
| 176. C79 | #13216 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773889 | 2 |
| #23765137 | 2 |
| #23765127 | 2 |
| #23765120 | 2 |
| #23765004 | 2 |
| #23763525 | 2 |
| C2×#362×C79 | 2 |
| #13216 | 79 |