Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
430 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 4. C2×#19098367 | C2 | semidirect |
| 5. #23764186 | C2 | semidirect |
| 6. #23761490 | C2 | semidirect |
| 7. C2×#362×C79 | C2 | semidirect |
| 182. C2×#362 | D79 | semidirect |
| 188. C79 | #13412 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773889 | 2 |
| C2×#19098369 | 2 |
| #23765113 | 2 |
| C2×#19098367 | 2 |
| #23764186 | 2 |
| #23761490 | 2 |
| C2×#362×C79 | 2 |
| #13412 | 79 |