Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
742 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 742 conjugacy classes of subgroups — too many to draw. Only its 139 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 |
|---|---|---|
| 2. C2×#19098764 | C2 | semidirect |
| 3. #23764336 | C2 | semidirect |
| 4. C2×#19098306 | C2 | semidirect |
| 5. C79×#1277 | C2 | semidirect |
| 51. C2×Dic158 | D8 | semidirect |
| 83. C2×C8×C79 | SD16 | semidirect |
| 150. #1277 | D79 | semidirect |
| 151. C79 | #10262 | semidirect |
| 225. C2×C8 | #11929613 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098940 | 2 |
| C2×#19098764 | 2 |
| #23764336 | 2 |
| C2×#19098306 | 2 |
| C79×#1277 | 2 |
| #10262 | 79 |