Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1036 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1036 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. #22549787 | C2 | direct (N × H) |
| 3. C2×C127⋊#95 | C2 | semidirect |
| 4. C23×Q8×C127 | C2 | semidirect |
| 9. C127⋊#95 | C22 | semidirect |
| 11. C22×Q8×C127 | C22 | semidirect |
| 15. C23×D127 | Q8 | semidirect |
| 32. C22×D127 | C2×Q8 | semidirect |
| 56. C2×C127 | #393 | semidirect |
| 62. C127 | C2×#393 | semidirect |
| 63. C23×Q8 | D127 | semidirect |
| 69. C22×Q8 | C2×D127 | semidirect |
| 119. C2 | #22549787 | 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 |
| #22549787 | 2 |
| C2×C127⋊#95 | 2 |
| C23×Q8×C127 | 2 |
| C2×#393 | 127 |