Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
520 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 520 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 |
|---|---|---|
| 3. #23761730 | C2 | semidirect |
| 4. #23761306 | C2 | semidirect |
| 189. C79 | #9517 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772429 | 2 |
| #23761738 | 2 |
| #23761730 | 2 |
| #23761306 | 2 |
| C79×#2579 | 2 |
| #9517 | 79 |