Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
262 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 6. #19098339 | C4 | semidirect |
| 8. #19098316 | C4 | semidirect |
| 25. #106×C79 | C8 | semidirect |
| 91. C79 | #7175 | semidirect |
| 110. #106 | C79⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14579101 | 2 |
| #23762148 | 2 |
| C4×#106×C79 | 2 |
| #7175 | 79 |