Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
604 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 604 conjugacy classes of subgroups — too many to draw. Only its 171 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×#19098612 | C2 | semidirect |
| 3. #23765615 | C2 | direct (N × H) |
| 4. C2×#19098386 | C2 | semidirect |
| 5. C2×#19098377 | C2 | semidirect |
| 6. C2×#349×C79 | C2 | semidirect |
| 13. #19098612 | C22 | semidirect |
| 18. #19098386 | C22 | semidirect |
| 19. #19098377 | C22 | semidirect |
| 22. #349×C79 | C22 | semidirect |
| 150. C2×C79 | #2238 | semidirect |
| 158. C2×#349 | D79 | semidirect |
| 159. C79 | C2×#2238 | semidirect |
| 175. #349 | C2×D79 | semidirect |
| 303. C2 | #23765615 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098816 | 2 |
| C2×#19098612 | 2 |
| #23765615 | 2 |
| C2×#19098386 | 2 |
| C2×#19098377 | 2 |
| C2×#349×C79 | 2 |
| C2×#2238 | 79 |