Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1020 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 1020 conjugacy classes of subgroups — too many to draw. Only its 115 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. #23769516 | C2 | semidirect |
| 4. C2×#19098299 | C2 | semidirect |
| 6. #23761242 | C2 | semidirect |
| 7. C2×#328×C79 | C2 | semidirect |
| 111. C22×Dic79 | SD16 | semidirect |
| 271. C2×#328 | D79 | 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×#19098716 | 2 |
| C2×#19098713 | 2 |
| #23769516 | 2 |
| C2×#19098299 | 2 |
| #23761640 | 2 |
| #23761242 | 2 |
| C2×#328×C79 | 2 |
| #9966 | 79 |