Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
320 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 105 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 |
|---|---|---|
| 4. M16×Dic127 | C2 | semidirect |
| 5. #22549722 | C2 | semidirect |
| 6. #22549635 | C2 | semidirect |
| 7. #339×C127 | C2 | semidirect |
| 10. #16861174 | C4 | semidirect |
| 11. #16861171 | C4 | semidirect |
| 17. #16861137 | C4 | semidirect |
| 18. #16861135 | C4 | semidirect |
| 37. #14523232 | C2×C4 | semidirect |
| 44. C4×Dic127 | C2×C4 | semidirect |
| 50. M16×C127 | C2×C4 | semidirect |
| 56. C42×C127 | C2×C4 | semidirect |
| 107. C127 | #1759 | semidirect |
| 114. #339 | D127 | semidirect |
| 148. M16 | C4×D127 | semidirect |
| 163. C42 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550344 | 2 |
| C2×#16861137 | 2 |
| C2×#16861135 | 2 |
| M16×Dic127 | 2 |
| #22549722 | 2 |
| #22549635 | 2 |
| #339×C127 | 2 |
| #1759 | 127 |