Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
514 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 514 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#19098368 | C2 | semidirect |
| 4. #23763564 | C2 | semidirect |
| 5. C2×C4×C16×C79 | C2 | semidirect |
| 11. #19098947 | C4 | semidirect |
| 137. C2×C4×C16 | D79 | semidirect |
| 139. C79 | #13204 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098947 | 2 |
| C2×#19098368 | 2 |
| C2×#19098365 | 2 |
| #23763564 | 2 |
| C2×C4×C16×C79 | 2 |
| #13204 | 79 |