Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
354 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 354 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. #23765198 | C2 | semidirect |
| 3. #335×D79 | C2 | semidirect |
| 4. #23761455 | C2 | semidirect |
| 5. #23761447 | C2 | semidirect |
| 6. #23761445 | C2 | semidirect |
| 7. C79×#1364 | C2 | semidirect |
| 142. #1364 | D79 | semidirect |
| 145. C79 | #11947 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773980 | 2 |
| #23765198 | 2 |
| #335×D79 | 2 |
| #23761455 | 2 |
| #23761447 | 2 |
| #23761445 | 2 |
| C79×#1364 | 2 |
| #11947 | 79 |