Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
376 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 127 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. #23761516 | C2 | semidirect |
| 4. #23761498 | C2 | semidirect |
| 123. C79 | #12874 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765021 | 2 |
| #23763450 | 2 |
| #23761516 | 2 |
| #23761498 | 2 |
| C79×#2912 | 2 |
| #12874 | 79 |