Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
396 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 396 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. #23765189 | C2 | semidirect |
| 3. C2×#19098378 | C2 | semidirect |
| 4. C2×#19098368 | C2 | semidirect |
| 7. C79×#1382 | C2 | semidirect |
| 181. #1382 | D79 | semidirect |
| 182. C79 | #13388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773056 | 2 |
| #23765189 | 2 |
| C2×#19098378 | 2 |
| C2×#19098368 | 2 |
| C2×#19098346 | 2 |
| #23763461 | 2 |
| C79×#1382 | 2 |
| #13388 | 79 |