Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
652 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 652 conjugacy classes of subgroups — too many to draw. Only its 229 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×#16861166 | C2 | semidirect |
| 4. #22549774 | C2 | semidirect |
| 5. #22549767 | C2 | semidirect |
| 6. C4×C4⋊Dic127 | C2 | semidirect |
| 7. C4×(C2×D127)⋊C4 | C2 | semidirect |
| 8. C43×C127 | C2 | semidirect |
| 11. C4×D508 | C4 | semidirect |
| 51. C42×C127 | D4 | semidirect |
| 92. C4×C127 | #117 | semidirect |
| 103. C127 | #2293 | semidirect |
| 111. C43 | D127 | semidirect |
| 154. C42 | D508 | semidirect |
| 197. C4 | #16861166 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D508 | 2 |
| C2×#16861166 | 2 |
| #22549778 | 2 |
| #22549774 | 2 |
| #22549767 | 2 |
| C4×C4⋊Dic127 | 2 |
| C4×(C2×D127)⋊C4 | 2 |
| C43×C127 | 2 |
| #2293 | 127 |