Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
566 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23766691 | C2 | semidirect |
| 4. #23761830 | C2 | semidirect |
| 5. #23761829 | C2 | semidirect |
| 6. #23761228 | C2 | semidirect |
| 102. C4×Dic79 | SD16 | semidirect |
| 212. C79 | #10014 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773427 | 2 |
| #23766691 | 2 |
| #23764233 | 2 |
| #23761830 | 2 |
| #23761829 | 2 |
| #23761228 | 2 |
| C79×#3103 | 2 |
| #10014 | 79 |