Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
310 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 53 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. #23765620 | C2 | semidirect |
| 3. #23765617 | C2 | semidirect |
| 5. #23761387 | C2 | semidirect |
| 7. C79×#1340 | C2 | semidirect |
| 152. #1340 | D79 | semidirect |
| 154. C79 | #12302 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774292 | 2 |
| #23765620 | 2 |
| #23765617 | 2 |
| #23764954 | 2 |
| #23761387 | 2 |
| #23761337 | 2 |
| C79×#1340 | 2 |
| #12302 | 79 |