Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
500 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 500 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. C2×#19098612 | C2 | semidirect |
| 2. #23765128 | C2 | semidirect |
| 3. C2×#19098345 | C2 | semidirect |
| 4. #23761516 | C2 | semidirect |
| 31. #14579097 | D4 | semidirect |
| 160. C79 | #12998 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098612 | 2 |
| #23765128 | 2 |
| C2×#19098345 | 2 |
| #23761516 | 2 |
| C79×#3054 | 2 |
| #12998 | 79 |