Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
462 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 109 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. #23772317 | C2 | semidirect |
| 3. #23765129 | C2 | semidirect |
| 4. #23764296 | C2 | semidirect |
| 5. #23761495 | C2 | semidirect |
| 6. #23761490 | C2 | semidirect |
| 7. C79×#2145 | C2 | semidirect |
| 12. C2×#14579107 | C4 | semidirect |
| 13. C2×#14579105 | C4 | semidirect |
| 14. C2×#14579104 | C4 | semidirect |
| 15. C2×#14579102 | C4 | semidirect |
| 185. #2145 | D79 | semidirect |
| 190. C79 | #13016 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098993 | 2 |
| #23772317 | 2 |
| #23765129 | 2 |
| #23764296 | 2 |
| #23761495 | 2 |
| #23761490 | 2 |
| C79×#2145 | 2 |
| #13016 | 79 |