Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
792 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 792 conjugacy classes of subgroups — too many to draw. Only its 269 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. C23×C127⋊C8 | C2 | semidirect |
| 3. #22549844 | C2 | direct (N × H) |
| 4. C2×(C2×D127)⋊C8 | C2 | semidirect |
| 5. C22×M16×C127 | C2 | semidirect |
| 16. C22×C127⋊C8 | C22 | semidirect |
| 17. (C2×D127)⋊C8 | C22 | semidirect |
| 20. C2×M16×C127 | C22 | semidirect |
| 91. C2×C127 | #408 | semidirect |
| 96. C127 | C2×#408 | semidirect |
| 98. C22×M16 | D127 | semidirect |
| 112. C2×M16 | C2×D127 | semidirect |
| 188. C2 | #22549844 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523248 | 2 |
| C23×C127⋊C8 | 2 |
| #22549844 | 2 |
| C2×(C2×D127)⋊C8 | 2 |
| C22×M16×C127 | 2 |
| C2×#408 | 127 |