Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
852 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 852 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 1. #23774206 | C2 | semidirect |
| 2. C2×#19098714 | C2 | semidirect |
| 3. #23763321 | C2 | semidirect |
| 4. #23761763 | C2 | semidirect |
| 5. #23761760 | C2 | semidirect |
| 6. #23761288 | C2 | semidirect |
| 239. C79 | #9987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774206 | 2 |
| C2×#19098714 | 2 |
| #23763321 | 2 |
| #23761763 | 2 |
| #23761760 | 2 |
| #23761288 | 2 |
| C2×#447×C79 | 2 |
| #9987 | 79 |