Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
314 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 314 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. #23765174 | C2 | semidirect |
| 2. #23765156 | C2 | semidirect |
| 5. #23764148 | C2 | semidirect |
| 6. #23761513 | C2 | semidirect |
| 149. C79 | #13466 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765174 | 2 |
| #23765156 | 2 |
| #23765136 | 2 |
| #23765128 | 2 |
| #23764148 | 2 |
| #23761513 | 2 |
| C79×#1974 | 2 |
| #13466 | 79 |