Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
642 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 87 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. #23774778 | C2 | semidirect |
| 2. #23774315 | C2 | semidirect |
| 3. #23773852 | C2 | semidirect |
| 4. #23764240 | C2 | semidirect |
| 5. #23761818 | C2 | semidirect |
| 6. #23761290 | C2 | semidirect |
| 7. C79×#1525 | C2 | semidirect |
| 208. #1525 | D79 | semidirect |
| 211. C79 | #10104 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23774778 | 2 |
| #23774315 | 2 |
| #23773852 | 2 |
| #23764240 | 2 |
| #23761818 | 2 |
| #23761290 | 2 |
| C79×#1525 | 2 |
| #10104 | 79 |