Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
522 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 522 conjugacy classes of subgroups — too many to draw. Only its 131 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. #23765011 | C2 | semidirect |
| 2. #23761326 | C2 | semidirect |
| 6. C22⋊(C79⋊C16) | C22 | semidirect |
| 141. C79 | #11421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765011 | 2 |
| #23761326 | 2 |
| C2×#408×C79 | 2 |
| #11421 | 79 |