Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
296 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 61 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. #23765639 | C2 | semidirect |
| 3. #23762925 | C2 | semidirect |
| 4. #23761444 | C2 | semidirect |
| 5. #23761381 | C2 | semidirect |
| 6. #23761367 | C2 | semidirect |
| 7. C79×#2224 | C2 | semidirect |
| 149. #2224 | D79 | semidirect |
| 154. C79 | #12388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776486 | 2 |
| #23765639 | 2 |
| #23762925 | 2 |
| #23761444 | 2 |
| #23761381 | 2 |
| #23761367 | 2 |
| C79×#2224 | 2 |
| #12388 | 79 |