Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
432 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 432 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23764123 | C2 | semidirect |
| 3. #23762171 | C2 | semidirect |
| 6. #23761302 | C2 | semidirect |
| 7. C79×#1281 | C2 | semidirect |
| 171. #1281 | 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 |
|---|---|
| #23772119 | 2 |
| #23764123 | 2 |
| #23762171 | 2 |
| #23761896 | 2 |
| #23761800 | 2 |
| #23761302 | 2 |
| C79×#1281 | 2 |
| #8880 | 79 |