Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
408 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 91 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×#19098388 | C2 | semidirect |
| 3. C2×#19098370 | C2 | semidirect |
| 4. C2×#19098348 | C2 | semidirect |
| 5. #23763465 | C2 | semidirect |
| 6. #23761509 | C2 | semidirect |
| 7. C79×#2139 | C2 | semidirect |
| 44. C2×C79⋊C16 | D4 | semidirect |
| 187. #2139 | D79 | semidirect |
| 191. C79 | #13384 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773066 | 2 |
| C2×#19098388 | 2 |
| C2×#19098370 | 2 |
| C2×#19098348 | 2 |
| #23763465 | 2 |
| #23761509 | 2 |
| C79×#2139 | 2 |
| #13384 | 79 |