Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
436 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 436 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 |
|---|---|---|
| 2. #23761991 | C2 | semidirect |
| 3. #23761818 | C2 | semidirect |
| 4. #23761689 | C2 | semidirect |
| 5. C4×#108×C79 | C2 | semidirect |
| 136. C4×#108 | D79 | semidirect |
| 140. C79 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773979 | 2 |
| #23761991 | 2 |
| #23761818 | 2 |
| #23761689 | 2 |
| C4×#108×C79 | 2 |
| #9726 | 79 |