Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 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. #22549832 | C2 | semidirect |
| 3. C4×#14523232 | C2 | semidirect |
| 4. C2×C4×C127⋊C8 | C2 | semidirect |
| 6. #16861216 | C4 | direct (N × H) |
| 18. #14523232 | C2×C4 | semidirect |
| 19. C2×C127⋊C8 | C2×C4 | semidirect |
| 48. C4×C127 | #131 | semidirect |
| 54. C127 | C4×#131 | semidirect |
| 102. C4 | #16861216 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861216 | 2 |
| #22549832 | 2 |
| C4×#14523232 | 2 |
| C2×C4×C127⋊C8 | 2 |
| C4×#41×C127 | 2 |
| C4×#131 | 127 |