Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
444 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 3. #23761387 | C2 | direct (N × H) |
| 5. C22×Dic316 | C4 | semidirect |
| 10. #19098821 | C4 | semidirect |
| 12. C2×#14579093 | C4 | semidirect |
| 24. C2×Dic316 | C2×C4 | semidirect |
| 36. #14579093 | C2×C4 | semidirect |
| 165. C2×C79 | #1340 | semidirect |
| 171. C79 | C2×#1340 | semidirect |
| 331. C2 | #23761387 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098821 | 2 |
| C2×#19098345 | 2 |
| #23761387 | 2 |
| C2×H(3,ℤ/4)×C79 | 2 |
| C2×#1340 | 79 |