Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
406 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #23762014 | C2 | semidirect |
| 5. #23761820 | C2 | semidirect |
| 6. #23761271 | C2 | semidirect |
| 7. C79×#1302 | C2 | semidirect |
| 187. #1302 | D79 | semidirect |
| 189. C79 | #9314 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773563 | 2 |
| #23772049 | 2 |
| #23762014 | 2 |
| #23761835 | 2 |
| #23761820 | 2 |
| #23761271 | 2 |
| C79×#1302 | 2 |
| #9314 | 79 |