Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
888 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 101 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. #23774172 | C2 | semidirect |
| 3. #23764386 | C2 | semidirect |
| 5. #23761973 | C2 | semidirect |
| 6. #23761246 | C2 | semidirect |
| 248. C79 | #9955 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774172 | 2 |
| #23767047 | 2 |
| #23764386 | 2 |
| #23763331 | 2 |
| #23761973 | 2 |
| #23761246 | 2 |
| C2×#450×C79 | 2 |
| #9955 | 79 |