Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
436 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 436 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 2. C4×#14579096 | C2 | semidirect |
| 3. #23761992 | C2 | semidirect |
| 4. #23761991 | C2 | semidirect |
| 5. #23761816 | C2 | semidirect |
| 6. #23761690 | C2 | semidirect |
| 7. C79×#1484 | C2 | semidirect |
| 189. #1484 | D79 | semidirect |
| 191. C79 | #9726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23773975 | 2 |
| C4×#14579096 | 2 |
| #23761992 | 2 |
| #23761991 | 2 |
| #23761816 | 2 |
| #23761690 | 2 |
| C79×#1484 | 2 |
| #9726 | 79 |