Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
1210 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 1210 conjugacy classes of subgroups — too many to draw. Only its 191 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 |
|---|---|---|
| 1. #23769121 | C2 | semidirect |
| 2. #23765984 | C2 | semidirect |
| 3. #23764566 | C2 | semidirect |
| 5. #23763859 | C2 | semidirect |
| 6. #23763813 | C2 | semidirect |
| 7. #23763477 | C2 | semidirect |
| 217. C79 | #23989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23769121 | 2 |
| #23765984 | 2 |
| #23764566 | 2 |
| #23764529 | 2 |
| #23763859 | 2 |
| #23763813 | 2 |
| #23763477 | 2 |
| C79×#3491 | 2 |
| #23989 | 79 |