Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
400 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #23764390 | C2 | semidirect |
| 5. #23761310 | C2 | semidirect |
| 6. #23761271 | C2 | semidirect |
| 7. C79×#1556 | C2 | semidirect |
| 182. #1556 | D79 | semidirect |
| 186. C79 | #9338 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774621 | 2 |
| #23772572 | 2 |
| #23764390 | 2 |
| #23762008 | 2 |
| #23761310 | 2 |
| #23761271 | 2 |
| C79×#1556 | 2 |
| #9338 | 79 |