Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
398 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 97 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. #23762172 | C2 | semidirect |
| 3. #23762057 | C2 | semidirect |
| 4. #23761964 | C2 | semidirect |
| 6. #23761260 | C2 | semidirect |
| 180. C79 | #10468 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23763410 | 2 |
| #23762172 | 2 |
| #23762057 | 2 |
| #23761964 | 2 |
| #23761721 | 2 |
| #23761260 | 2 |
| C79×#3077 | 2 |
| #10468 | 79 |