Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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. #23764124 | C2 | semidirect |
| 3. #23762172 | C2 | semidirect |
| 6. #23761244 | C2 | semidirect |
| 7. C79×#1303 | C2 | semidirect |
| 170. #1303 | D79 | semidirect |
| 172. C79 | #8880 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23772117 | 2 |
| #23764124 | 2 |
| #23762172 | 2 |
| #23761894 | 2 |
| #23761800 | 2 |
| #23761244 | 2 |
| C79×#1303 | 2 |
| #8880 | 79 |