Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
420 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 99 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. #23762038 | C2 | semidirect |
| 3. #23761951 | C2 | semidirect |
| 5. #23761272 | C2 | semidirect |
| 6. #23761265 | C2 | semidirect |
| 20. #500×C79 | C4 | semidirect |
| 21. #492×C79 | C4 | semidirect |
| 22. #487×C79 | C4 | semidirect |
| 23. #486×C79 | C4 | semidirect |
| 167. C79 | #9415 | semidirect |
| 170. #500 | Dic79 | semidirect |
| 171. #492 | Dic79 | semidirect |
| 172. #487 | Dic79 | semidirect |
| 173. #486 | Dic79 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772471 | 2 |
| #23762038 | 2 |
| #23761951 | 2 |
| #23761947 | 2 |
| #23761272 | 2 |
| #23761265 | 2 |
| C79×#3182 | 2 |
| #9415 | 79 |