Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
150 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 150 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 10. #16861155 | C4 | direct (N × H) |
| 55. C4×C127 | Q32 | semidirect |
| 64. C127 | C4×Q32 | semidirect |
| 121. C4 | #16861155 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861155 | 2 |
| C4×Dic508 | 2 |
| #22549701 | 2 |
| #22549680 | 2 |
| #22549679 | 2 |
| C4×C127⋊C16 | 2 |
| C4×Q16×C127 | 2 |
| C4×Q32 | 127 |