Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
888 conjugacy classes of subgroups; only the 429 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 429 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. #22549745 | C2 | direct (N × H) |
| 12. C2×C4×Dic127 | C4 | semidirect |
| 27. C4×Dic127 | C2×C4 | semidirect |
| 40. C2×Dic127 | C4⋊C4 | semidirect |
| 53. C2×C4×C127 | C4⋊C4 | semidirect |
| 68. C4×C127 | C2×C4⋊C4 | semidirect |
| 70. Dic127 | C2×C4⋊C4 | semidirect |
| 71. C2×C127 | #384 | semidirect |
| 78. C127 | C2×#384 | semidirect |
| 131. C2×C4 | Dic127⋊C4 | semidirect |
| 148. C4 | C2×Dic127⋊C4 | semidirect |
| 149. C2 | #22549745 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic127 | 2 |
| C22×Dic127⋊C4 | 2 |
| C22×C4×Dic127 | 2 |
| #22549745 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C2×#384 | 127 |