Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 93 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. #23765188 | C2 | semidirect |
| 3. C2×#19098364 | C2 | semidirect |
| 4. C2×#19098348 | C2 | semidirect |
| 5. #23763461 | C2 | semidirect |
| 6. #23761497 | C2 | semidirect |
| 7. C2×#361×C79 | C2 | semidirect |
| 64. M32×C79 | D4 | semidirect |
| 186. C2×#361 | D79 | semidirect |
| 191. C79 | #13387 | semidirect |
| 236. M32 | C22⋊D79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773044 | 2 |
| #23765188 | 2 |
| C2×#19098364 | 2 |
| C2×#19098348 | 2 |
| #23763461 | 2 |
| #23761497 | 2 |
| C2×#361×C79 | 2 |
| #13387 | 79 |