Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
334 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 1. #23765216 | C2 | semidirect |
| 2. #23761338 | C2 | semidirect |
| 3. #23761336 | C2 | semidirect |
| 127. C79 | #11538 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765216 | 2 |
| #23761338 | 2 |
| #23761336 | 2 |
| C79×#2930 | 2 |
| #11538 | 79 |