Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
480 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 480 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 |
|---|---|---|
| 3. #22549981 | C2 | direct (N × H) |
| 10. C2×#14523238 | C4 | semidirect |
| 36. #14523238 | C2×C4 | semidirect |
| 98. C2×C127 | #441 | semidirect |
| 103. C127 | C2×#441 | semidirect |
| 201. C2 | #22549981 | 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×C4×Dic254 | 2 |
| #22549981 | 2 |
| C2×#16861140 | 2 |
| C2×#16861133 | 2 |
| C2×#16861132 | 2 |
| C2×#16861120 | 2 |
| C2×C4×Q8×C127 | 2 |
| C2×#441 | 127 |