Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
288 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 288 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 85. C2×C4×C127 | Q16 | semidirect |
| 117. C127 | #2056 | semidirect |
| 200. C2×C4 | #14523238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523238 | 2 |
| C2×C4⋊(C127⋊C8) | 2 |
| C2×#16861133 | 2 |
| C2×#16861132 | 2 |
| #22549782 | 2 |
| #22549638 | 2 |
| #391×C127 | 2 |
| #2056 | 127 |