Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
428 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 428 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 |
|---|---|---|
| 2. #23765188 | C2 | semidirect |
| 3. C2×#19098377 | C2 | semidirect |
| 4. C2×#19098365 | C2 | semidirect |
| 5. #23763464 | C2 | semidirect |
| 6. #23761496 | C2 | semidirect |
| 7. C2×#350×C79 | C2 | semidirect |
| 63. M32×C79 | D4 | semidirect |
| 188. C2×#350 | 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 |
|---|---|
| #23773048 | 2 |
| #23765188 | 2 |
| C2×#19098377 | 2 |
| C2×#19098365 | 2 |
| #23763464 | 2 |
| #23761496 | 2 |
| C2×#350×C79 | 2 |
| #13387 | 79 |