Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
680 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 680 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 |
|---|---|---|
| 2. #22549643 | C2 | direct (N × H) |
| 7. C2×C22⋊Dic127 | C4 | semidirect |
| 10. C23×C4×C127 | C4 | semidirect |
| 13. C2×C22⋊C4×C127 | C4 | semidirect |
| 20. C22⋊Dic127 | C2×C4 | semidirect |
| 33. C22×C4×C127 | C2×C4 | semidirect |
| 99. C2×C127 | #342 | semidirect |
| 103. C127 | C2×#342 | semidirect |
| 109. C23×C4 | Dic127 | semidirect |
| 116. C2×C22⋊C4 | Dic127 | semidirect |
| 133. C22×C4 | C2×Dic127 | semidirect |
| 202. C2 | #22549643 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic127 | 2 |
| #22549643 | 2 |
| C22×C22⋊C4×C127 | 2 |
| C2×#342 | 127 |