Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
158 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 3. Q16×Dic127 | C2 | semidirect |
| 4. Dic127⋊C16 | C2 | semidirect |
| 5. #22549680 | C2 | semidirect |
| 7. C2×Q32×C127 | C2 | semidirect |
| 73. C127 | #2211 | semidirect |
| 74. C2×Q32 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861152 | 2 |
| #22550261 | 2 |
| Q16×Dic127 | 2 |
| Dic127⋊C16 | 2 |
| #22549680 | 2 |
| #22549678 | 2 |
| C2×Q32×C127 | 2 |
| #2211 | 127 |