Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
392 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 95 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. #23762165 | C2 | semidirect |
| 4. #23761293 | C2 | semidirect |
| 14. #19098303 | C4 | semidirect |
| 15. #19098303 | C4 | semidirect |
| 16. #19098303 | C4 | semidirect |
| 143. C79 | #8918 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772471 | 2 |
| #23762165 | 2 |
| #23761992 | 2 |
| #23761293 | 2 |
| C79×#1963 | 2 |
| #8918 | 79 |