Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
400 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23763438 | C2 | semidirect |
| 3. #23761419 | C2 | semidirect |
| 4. #23761416 | C2 | semidirect |
| 5. C2×C22⋊C16×C79 | C2 | semidirect |
| 169. C2×C22⋊C16 | D79 | semidirect |
| 173. C79 | #11893 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772981 | 2 |
| #23763438 | 2 |
| #23761419 | 2 |
| #23761416 | 2 |
| C2×C22⋊C16×C79 | 2 |
| #11893 | 79 |