Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 2. C2×Dic1016 | C2 | semidirect |
| 3. C2×#16861153 | C2 | semidirect |
| 4. #22550118 | C2 | semidirect |
| 5. #22549679 | C2 | semidirect |
| 6. (C2×D127)⋊C16 | C2 | semidirect |
| 7. #357×C127 | C2 | semidirect |
| 86. C127 | #2189 | semidirect |
| 92. #357 | D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861228 | 2 |
| C2×Dic1016 | 2 |
| C2×#16861153 | 2 |
| #22550118 | 2 |
| #22549679 | 2 |
| (C2×D127)⋊C16 | 2 |
| #357×C127 | 2 |
| #2189 | 127 |