Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
348 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#16861119 | C2 | semidirect |
| 3. C2×C8×Dic127 | C2 | semidirect |
| 5. #22549630 | C2 | semidirect |
| 6. #22549630 | C2 | semidirect |
| 10. C2×#14523232 | C4 | semidirect |
| 22. C22⋊C8×C127 | C4 | semidirect |
| 57. C2×Dic127 | M16 | semidirect |
| 59. C127⋊C8 | C22⋊C4 | semidirect |
| 105. C127 | #1753 | semidirect |
| 124. C22⋊C8 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523232 | 2 |
| C2×#16861119 | 2 |
| C2×C8×Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| #22549630 | 2 |
| C2×C22⋊C8×C127 | 2 |
| #1753 | 127 |