Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
676 conjugacy classes of subgroups; only the 151 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 151 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×#19098992 | C2 | semidirect |
| 2. #23775121 | C2 | semidirect |
| 3. #23765653 | C2 | semidirect |
| 4. #23765492 | C2 | semidirect |
| 5. #23765445 | C2 | semidirect |
| 6. #23765341 | C2 | semidirect |
| 7. C16×D316 | C2 | semidirect |
| 8. C4×D16×C79 | C2 | semidirect |
| 52. D16×C79 | D4 | semidirect |
| 121. C4×C79 | #508 | semidirect |
| 138. C4×D16 | D79 | semidirect |
| 140. C79 | #33849 | semidirect |
| 179. D16 | D316 | semidirect |
| 255. C4 | #19098992 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098992 | 2 |
| #23775121 | 2 |
| #23765653 | 2 |
| #23765492 | 2 |
| #23765445 | 2 |
| #23765341 | 2 |
| C16×D316 | 2 |
| C4×D16×C79 | 2 |
| #33849 | 79 |