Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
138 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 138 conjugacy classes of subgroups — too many to draw. Only its 27 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. #23761573 | C2 | semidirect |
| 2. #23761435 | C2 | semidirect |
| 71. C79 | #7525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23761573 | 2 |
| #23761435 | 2 |
| C79×#1662 | 2 |
| #7525 | 79 |