Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
670 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 670 conjugacy classes of subgroups — too many to draw. Only its 151 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. C2×#19098943 | C2 | semidirect |
| 3. #23764360 | C2 | semidirect |
| 4. C79⋊#1273 | C2 | semidirect |
| 131. C79 | #10306 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098943 | 2 |
| C2×#19098909 | 2 |
| #23764360 | 2 |
| C79⋊#1273 | 2 |
| C79×#1957 | 2 |
| #10306 | 79 |