Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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. #23761505 | C2 | semidirect |
| 4. #23761501 | C2 | semidirect |
| 10. #19098601 | C4 | semidirect |
| 12. C2×#14579093 | C4 | semidirect |
| 123. C79 | #12873 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23771995 | 2 |
| #23765021 | 2 |
| #23761505 | 2 |
| #23761501 | 2 |
| C79×#1812 | 2 |
| #12873 | 79 |