Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
136 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 2. #23761474 | C2 | semidirect |
| 3. C79×C4⋊C32 | C2 | semidirect |
| 68. C4⋊C32 | D79 | semidirect |
| 70. C79 | #7446 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23765661 | 2 |
| #23761474 | 2 |
| C79×C4⋊C32 | 2 |
| #7446 | 79 |