Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
474 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 474 conjugacy classes of subgroups — too many to draw. Only its 83 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. #23761565 | C2 | direct (N × H) |
| 8. C2×C4⋊Q8×C79 | C4 | semidirect |
| 11. #492×C79 | C4 | semidirect |
| 13. C2×C4×C8×C79 | C4 | semidirect |
| 27. C4⋊Q8×C79 | C2×C4 | semidirect |
| 35. C4×C8×C79 | C2×C4 | semidirect |
| 114. C2×C79 | #1409 | semidirect |
| 119. C79 | C2×#1409 | semidirect |
| 121. C2×C4⋊Q8 | Dic79 | semidirect |
| 124. #492 | Dic79 | semidirect |
| 127. C2×C4×C8 | Dic79 | semidirect |
| 140. C4⋊Q8 | C2×Dic79 | semidirect |
| 151. C4×C8 | C2×Dic79 | semidirect |
| 229. C2 | #23761565 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19098356 | 2 |
| #23761565 | 2 |
| C2×#492×C79 | 2 |
| C2×#1409 | 79 |