Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
194 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23761601 | C2 | semidirect |
| 4. #23761599 | C2 | semidirect |
| 7. #19098397 | C4 | semidirect |
| 20. C79⋊C32 | C2×C4 | semidirect |
| 76. C79 | #13634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098397 | 2 |
| #23765184 | 2 |
| #23761601 | 2 |
| #23761599 | 2 |
| C2×#366×C79 | 2 |
| #13634 | 79 |