Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
588 conjugacy classes of subgroups; only the 249 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 249 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 |
|---|---|---|
| 9. #16861209 | C4 | semidirect |
| 35. C4×Dic127 | Q8 | semidirect |
| 69. C4×C127 | C4×Q8 | semidirect |
| 73. Dic127 | C4⋊Q8 | semidirect |
| 80. C127 | C4×C4⋊Q8 | semidirect |
| 153. C4 | #16861174 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861209 | 2 |
| C2×#16861174 | 2 |
| #22549781 | 2 |
| #22549772 | 2 |
| C4⋊C4×Dic127 | 2 |
| C42×Dic127 | 2 |
| #384×C127 | 2 |
| C4×C4⋊Q8 | 127 |