Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
820 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 171 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. #23774627 | C2 | semidirect |
| 2. #23773782 | C2 | semidirect |
| 3. #23762734 | C2 | semidirect |
| 4. #23762728 | C2 | semidirect |
| 5. #23762723 | C2 | semidirect |
| 6. #23762038 | C2 | semidirect |
| 7. #23762007 | C2 | semidirect |
| 210. C79 | #19005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774627 | 2 |
| #23773782 | 2 |
| #23762734 | 2 |
| #23762728 | 2 |
| #23762723 | 2 |
| #23762038 | 2 |
| #23762007 | 2 |
| C79×#3531 | 2 |
| #19005 | 79 |