Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
456 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 109 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×C22⋊(C127⋊C8) | C2 | semidirect |
| 3. #22549599 | C2 | direct (N × H) |
| 4. C2×C22⋊C8×C127 | C2 | semidirect |
| 15. C22⋊(C127⋊C8) | C22 | semidirect |
| 19. C22⋊C8×C127 | C22 | semidirect |
| 25. C23×D127 | C8 | semidirect |
| 59. C22×D127 | C2×C8 | semidirect |
| 111. C2×C127 | #323 | semidirect |
| 117. C127 | C2×#323 | semidirect |
| 120. C2×C22⋊C8 | D127 | semidirect |
| 136. C22⋊C8 | C2×D127 | semidirect |
| 229. C2 | #22549599 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×(C2×D127)⋊C4 | 2 |
| C2×C22⋊(C127⋊C8) | 2 |
| #22549599 | 2 |
| C2×C22⋊C8×C127 | 2 |
| C2×#323 | 127 |