Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
354 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23763308 | C2 | semidirect |
| 5. #23761498 | C2 | semidirect |
| 6. #23761483 | C2 | semidirect |
| 7. C2×#365×C79 | C2 | semidirect |
| 15. #19098377 | C4 | semidirect |
| 137. C2×#365 | D79 | semidirect |
| 144. C79 | #13138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098377 | 2 |
| C2×#19098375 | 2 |
| #23764274 | 2 |
| #23763308 | 2 |
| #23761498 | 2 |
| #23761483 | 2 |
| C2×#365×C79 | 2 |
| #13138 | 79 |