Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
364 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23765203 | C2 | semidirect |
| 2. C4×#14579097 | C2 | semidirect |
| 3. #23761415 | C2 | semidirect |
| 126. C79 | #11751 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765203 | 2 |
| C4×#14579097 | 2 |
| #23761415 | 2 |
| C79×#3169 | 2 |
| #11751 | 79 |