Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
806 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 806 conjugacy classes of subgroups — too many to draw. Only its 155 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. #23777895 | C2 | semidirect |
| 3. #23762726 | C2 | semidirect |
| 4. #23762701 | C2 | semidirect |
| 5. #23762038 | C2 | semidirect |
| 6. #23762014 | C2 | semidirect |
| 156. C79 | #19063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23777895 | 2 |
| #23774594 | 2 |
| #23762726 | 2 |
| #23762701 | 2 |
| #23762038 | 2 |
| #23762014 | 2 |
| C79×#3135 | 2 |
| #19063 | 79 |