Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
512 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 107 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×#19098679 | C2 | semidirect |
| 3. #23765113 | C2 | semidirect |
| 4. #23764267 | C2 | semidirect |
| 5. #23761510 | C2 | semidirect |
| 6. #23761481 | C2 | semidirect |
| 7. C2×#361×C79 | C2 | semidirect |
| 11. #19098999 | C4 | semidirect |
| 81. Dic316 | C22⋊C4 | semidirect |
| 85. D632 | C22⋊C4 | semidirect |
| 188. C2×#361 | D79 | semidirect |
| 193. C79 | #13029 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098999 | 2 |
| C2×#19098679 | 2 |
| #23765113 | 2 |
| #23764267 | 2 |
| #23761510 | 2 |
| #23761481 | 2 |
| C2×#361×C79 | 2 |
| #13029 | 79 |