Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 65 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. #23762791 | C2 | semidirect |
| 5. #23761378 | C2 | semidirect |
| 6. #23761364 | C2 | semidirect |
| 7. C79×#2225 | C2 | semidirect |
| 131. #2225 | D79 | semidirect |
| 136. C79 | #12381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776410 | 2 |
| #23765625 | 2 |
| #23762791 | 2 |
| #23761447 | 2 |
| #23761378 | 2 |
| #23761364 | 2 |
| C79×#2225 | 2 |
| #12381 | 79 |