Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 125 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×#19098364 | C2 | semidirect |
| 2. C2×#19098364 | C2 | semidirect |
| 3. #23764133 | C2 | semidirect |
| 4. #23761478 | C2 | semidirect |
| 26. #14579095 | D4 | semidirect |
| 155. C79 | #13407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098364 | 2 |
| #23764133 | 2 |
| #23761478 | 2 |
| C2×#493×C79 | 2 |
| #13407 | 79 |