Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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. #23764197 | C2 | semidirect |
| 3. #23762098 | C2 | semidirect |
| 4. #23762016 | C2 | semidirect |
| 5. #23762011 | C2 | semidirect |
| 6. #23761740 | C2 | semidirect |
| 7. C79×#1551 | C2 | semidirect |
| 226. #1551 | D79 | semidirect |
| 230. C79 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777249 | 2 |
| #23764197 | 2 |
| #23762098 | 2 |
| #23762016 | 2 |
| #23762011 | 2 |
| #23761740 | 2 |
| C79×#1551 | 2 |
| #8458 | 79 |