Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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. C4⋊C8×D127 | C2 | semidirect |
| 3. #22549620 | C2 | semidirect |
| 4. #22549619 | C2 | semidirect |
| 5. #331×C127 | C2 | semidirect |
| 13. C4⋊(C127⋊C8) | C22 | semidirect |
| 16. C4⋊C8×C127 | C22 | semidirect |
| 74. D127 | #331 | direct (N × H) |
| 76. C127 | C2×#331 | semidirect |
| 81. #331 | D127 | direct (N × H) |
| 92. C4⋊C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #127×D127 | 2 |
| C4⋊C8×D127 | 2 |
| #22549620 | 2 |
| #22549619 | 2 |
| #331×C127 | 2 |
| C2×#331 | 127 |