Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
306 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 306 conjugacy classes of subgroups — too many to draw. Only its 75 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. #23765200 | C2 | semidirect |
| 3. #23763536 | C2 | semidirect |
| 4. #23761419 | C2 | semidirect |
| 5. #23761417 | C2 | semidirect |
| 157. C79 | #11866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773965 | 2 |
| #23765200 | 2 |
| #23763536 | 2 |
| #23761419 | 2 |
| #23761417 | 2 |
| #23761415 | 2 |
| C79×#1349 | 2 |
| #11866 | 79 |