Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 3. C2×#19098341 | C2 | semidirect |
| 4. #23761481 | C2 | semidirect |
| 5. C2×#347×C79 | C2 | semidirect |
| 15. #19098344 | C4 | semidirect |
| 136. C2×#347 | D79 | semidirect |
| 138. C79 | #12608 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098520 | 2 |
| C2×#19098344 | 2 |
| C2×#19098341 | 2 |
| #23761481 | 2 |
| C2×#347×C79 | 2 |
| #12608 | 79 |