Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
390 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23765174 | C2 | semidirect |
| 3. #23765127 | C2 | semidirect |
| 4. #23765108 | C2 | semidirect |
| 5. #23765013 | C2 | semidirect |
| 6. #23763455 | C2 | semidirect |
| 7. C79×#1381 | C2 | semidirect |
| 181. #1381 | D79 | semidirect |
| 182. C79 | #13406 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773121 | 2 |
| #23765174 | 2 |
| #23765127 | 2 |
| #23765108 | 2 |
| #23765013 | 2 |
| #23763455 | 2 |
| C79×#1381 | 2 |
| #13406 | 79 |