Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
160 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 160 conjugacy classes of subgroups — too many to draw. Only its 53 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×#16861154 | C2 | semidirect |
| 2. #22550117 | C2 | semidirect |
| 4. #22549702 | C2 | semidirect |
| 5. #22549681 | C2 | semidirect |
| 6. #22549678 | C2 | semidirect |
| 7. C2×M32×C127 | C2 | semidirect |
| 39. C16×C127 | D4 | semidirect |
| 76. C127 | #2220 | semidirect |
| 78. C2×M32 | D127 | semidirect |
| 115. C16 | C22⋊D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861154 | 2 |
| #22550117 | 2 |
| #22550112 | 2 |
| #22549702 | 2 |
| #22549681 | 2 |
| #22549678 | 2 |
| C2×M32×C127 | 2 |
| #2220 | 127 |