Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
318 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 91 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 |
|---|---|---|
| 5. C2×#14579097 | C4 | semidirect |
| 6. C2×#14579097 | C4 | semidirect |
| 9. #19098345 | C4 | semidirect |
| 136. C79 | #7256 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098345 | 2 |
| #23763442 | 2 |
| C2×H(3,ℤ/4)×C79 | 2 |
| #7256 | 79 |