Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
362 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16861142 | C2 | semidirect |
| 4. #22549772 | C2 | semidirect |
| 5. #22549639 | C2 | semidirect |
| 6. #22549630 | C2 | semidirect |
| 18. #16861130 | C4 | semidirect |
| 33. C2×C127⋊C8 | C2×C4 | semidirect |
| 36. C4⋊Dic127 | C2×C4 | semidirect |
| 81. D4×C127 | C4⋊C4 | semidirect |
| 124. C127 | #1862 | semidirect |
| 191. D4 | Dic127⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D4×Dic127 | 2 |
| C2×#16861142 | 2 |
| C2×#16861130 | 2 |
| #22549772 | 2 |
| #22549639 | 2 |
| #22549630 | 2 |
| C2×#102×C127 | 2 |
| #1862 | 127 |