Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1020 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 117 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. #23769516 | C2 | semidirect |
| 3. C2×#19098301 | C2 | semidirect |
| 4. C2×#19098300 | C2 | semidirect |
| 6. #23761242 | C2 | semidirect |
| 95. C22×Dic79 | SD16 | semidirect |
| 274. C79 | #9966 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098714 | 2 |
| #23769516 | 2 |
| C2×#19098301 | 2 |
| C2×#19098300 | 2 |
| #23761641 | 2 |
| #23761242 | 2 |
| C2×#450×C79 | 2 |
| #9966 | 79 |