Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
308 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 63 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. #23765447 | C2 | semidirect |
| 5. #23761382 | C2 | semidirect |
| 6. #23761369 | C2 | semidirect |
| 7. C79×#1690 | C2 | semidirect |
| 152. #1690 | D79 | semidirect |
| 156. C79 | #12339 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23776481 | 2 |
| #23765669 | 2 |
| #23765447 | 2 |
| #23761442 | 2 |
| #23761382 | 2 |
| #23761369 | 2 |
| C79×#1690 | 2 |
| #12339 | 79 |