Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
488 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 4. #22549968 | C2 | direct (N × H) |
| 10. C2×#14523238 | C4 | semidirect |
| 38. #14523238 | C2×C4 | semidirect |
| 68. C2×Dic127 | Q16 | semidirect |
| 97. Dic127 | C2×Q16 | semidirect |
| 98. C2×C127 | C4×Q16 | semidirect |
| 103. C127 | C2×C4×Q16 | semidirect |
| 201. C2 | #22549968 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523238 | 2 |
| C2×Q8×Dic127 | 2 |
| C2×#16861174 | 2 |
| #22549968 | 2 |
| C2×#16861142 | 2 |
| C2×#16861134 | 2 |
| C2×C8×Dic127 | 2 |
| C2×#103×C127 | 2 |
| C2×C4×Q16 | 127 |