Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
564 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 75 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. C2×#19098356 | C2 | semidirect |
| 3. #23761546 | C2 | direct (N × H) |
| 4. C2×#331×C79 | C2 | semidirect |
| 5. C2×#14579206 | C4 | semidirect |
| 9. #19098730 | C4 | semidirect |
| 12. C2×#14579078 | C4 | semidirect |
| 15. #19098356 | C22 | semidirect |
| 19. #331×C79 | C22 | semidirect |
| 23. #14579206 | C2×C4 | semidirect |
| 38. #14579078 | C2×C4 | semidirect |
| 195. C2×C79 | #1402 | semidirect |
| 200. C2×#331 | D79 | semidirect |
| 202. C79 | C2×#1402 | semidirect |
| 217. #331 | C2×D79 | semidirect |
| 393. C2 | #23761546 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098730 | 2 |
| C2×#19098356 | 2 |
| #23761546 | 2 |
| C2×#331×C79 | 2 |
| C2×#1402 | 79 |