Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
712 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 269 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. #22549742 | C2 | semidirect |
| 4. #22549741 | C2 | semidirect |
| 5. #22549740 | C2 | semidirect |
| 7. #382×C127 | C2 | semidirect |
| 16. C42×D127 | C4 | semidirect |
| 35. C4×Dic127 | C2×C4 | semidirect |
| 36. C4×Dic127 | C2×C4 | semidirect |
| 41. C42×C127 | C2×C4 | semidirect |
| 82. D127 | #382 | direct (N × H) |
| 84. C127 | C2×#382 | semidirect |
| 90. #382 | D127 | direct (N × H) |
| 125. C42 | C4×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊C4×D127 | 2 |
| C2×C42×D127 | 2 |
| #22549742 | 2 |
| #22549741 | 2 |
| #22549740 | 2 |
| #95×D127 | 2 |
| #382×C127 | 2 |
| C2×#382 | 127 |