Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
568 conjugacy classes of subgroups; only the 333 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 333 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 |
|---|---|---|
| 14. C4×Q8×C127 | C4 | semidirect |
| 22. C4⋊Dic127 | Q8 | direct (N × H) |
| 39. Q8×C127 | C4⋊C4 | semidirect |
| 58. C4×C127 | C4×Q8 | semidirect |
| 69. C127 | Q8×C4⋊C4 | semidirect |
| 77. C4×Q8 | Dic127 | semidirect |
| 102. Q8 | C4⋊Dic127 | direct (N × H) |
| 129. C4 | Q8×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic127 | 2 |
| #22549775 | 2 |
| #22549746 | 2 |
| C4×C4⋊Dic127 | 2 |
| C2×C4×Q8×C127 | 2 |
| Q8×C4⋊C4 | 127 |