Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
366 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 366 conjugacy classes of subgroups — too many to draw. Only its 91 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×#19098341 | C2 | semidirect |
| 3. #23761432 | C2 | direct (N × H) |
| 4. C2×#347×C79 | C2 | semidirect |
| 15. #19098341 | C22 | semidirect |
| 19. #347×C79 | C22 | semidirect |
| 121. C2×C79 | #1355 | semidirect |
| 126. C2×#347 | D79 | semidirect |
| 128. C79 | C2×#1355 | semidirect |
| 143. #347 | C2×D79 | semidirect |
| 245. C2 | #23761432 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098928 | 2 |
| C2×#19098341 | 2 |
| #23761432 | 2 |
| C2×#347×C79 | 2 |
| C2×#1355 | 79 |