Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
936 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 936 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×#19098372 | C2 | semidirect |
| 3. #23765110 | C2 | semidirect |
| 4. C2×#19098345 | C2 | semidirect |
| 5. C79×#1809 | C2 | semidirect |
| 9. #19099363 | C4 | semidirect |
| 14. C2×#14579101 | C22 | semidirect |
| 20. C2×#107×C79 | C22 | semidirect |
| 21. C2×#106×C79 | C22 | semidirect |
| 98. Dic316 | C22⋊C4 | semidirect |
| 104. D632 | C22⋊C4 | semidirect |
| 211. #1809 | D79 | semidirect |
| 212. C79 | #12739 | semidirect |
| 223. C2×#107 | C2×D79 | semidirect |
| 224. C2×#106 | C2×D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099363 | 2 |
| C2×#19098372 | 2 |
| #23765110 | 2 |
| C2×#19098345 | 2 |
| C79×#1809 | 2 |
| #12739 | 79 |