Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
710 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 1. #23776032 | C2 | semidirect |
| 2. #23775065 | C2 | semidirect |
| 3. #23762862 | C2 | semidirect |
| 4. #23762841 | C2 | semidirect |
| 5. #23762646 | C2 | semidirect |
| 6. #23762462 | C2 | semidirect |
| 7. #23762286 | C2 | semidirect |
| 8. C8×Dic316 | C2 | semidirect |
| 9. C79×#1706 | C2 | semidirect |
| 95. Dic316 | D8 | semidirect |
| 184. #1706 | D79 | semidirect |
| 191. C79 | #19888 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776032 | 2 |
| #23775065 | 2 |
| #23762862 | 2 |
| #23762841 | 2 |
| #23762646 | 2 |
| #23762462 | 2 |
| #23762286 | 2 |
| C8×Dic316 | 2 |
| C79×#1706 | 2 |
| #19888 | 79 |