Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
174 conjugacy classes of subgroups; only the 37 normal subgroups are shown.
This group has 174 conjugacy classes of subgroups — too many to draw. Only its 37 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 |
|---|---|---|
| 4. #19098612 | C4 | semidirect |
| 8. #19098320 | C4 | semidirect |
| 81. C79 | #7438 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23764953 | 2 |
| #23761521 | 2 |
| C79×#1315 | 2 |
| #7438 | 79 |