Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
814 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 814 conjugacy classes of subgroups — too many to draw. Only its 179 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. C2×#19099005 | C2 | semidirect |
| 3. #494×D79 | C2 | semidirect |
| 4. #23765668 | C2 | semidirect |
| 5. #23765657 | C2 | semidirect |
| 6. #23765656 | C2 | semidirect |
| 7. #23765652 | C2 | semidirect |
| 8. C4×#14579100 | C2 | semidirect |
| 9. C79×#2247 | C2 | semidirect |
| 64. #14579100 | D4 | semidirect |
| 157. C4×C79 | #510 | semidirect |
| 175. #2247 | D79 | semidirect |
| 177. C79 | #33718 | semidirect |
| 328. C4 | #19099005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19099005 | 2 |
| #23773829 | 2 |
| #494×D79 | 2 |
| #23765668 | 2 |
| #23765657 | 2 |
| #23765656 | 2 |
| #23765652 | 2 |
| C4×#14579100 | 2 |
| C79×#2247 | 2 |
| #33718 | 79 |