Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16861240 | C2 | semidirect |
| 3. C2×Q8×Dic127 | C2 | semidirect |
| 4. #22550100 | C2 | semidirect |
| 5. #22550096 | C2 | semidirect |
| 6. #22550084 | C2 | semidirect |
| 7. #22550074 | C2 | semidirect |
| 8. #22549899 | C2 | semidirect |
| 9. #22549878 | C2 | semidirect |
| 10. #22549877 | C2 | semidirect |
| 11. C2×#137×C127 | C2 | semidirect |
| 80. C2×Q8×C127 | D4 | semidirect |
| 150. Dic127 | #137 | semidirect |
| 158. C127 | #3037 | semidirect |
| 160. C2×#137 | D127 | semidirect |
| 210. C2×Q8 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861240 | 2 |
| #22550422 | 2 |
| C2×Q8×Dic127 | 2 |
| #22550100 | 2 |
| #22550096 | 2 |
| #22550084 | 2 |
| #22550074 | 2 |
| #22549899 | 2 |
| #22549878 | 2 |
| #22549877 | 2 |
| C2×#137×C127 | 2 |
| #3037 | 127 |