Finite Group DatabasebetaFinite Group DatabasebetaOrder 20224.
134 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 51 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×Dic1264 | C2 | semidirect |
| 3. #23761616 | C2 | direct (N × H) |
| 4. C2×C64×C79 | C2 | semidirect |
| 8. Dic1264 | C22 | semidirect |
| 12. C64×C79 | C22 | semidirect |
| 47. C2×C79 | SD128 | semidirect |
| 53. C2×C64 | D79 | semidirect |
| 54. C79 | C2×SD128 | semidirect |
| 62. C64 | C2×D79 | semidirect |
| 97. C2 | #23761616 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1264 | 2 |
| C2×D2528 | 2 |
| #23761616 | 2 |
| C2×C64×C79 | 2 |
| C2×SD128 | 79 |