Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
618 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 618 conjugacy classes of subgroups — too many to draw. Only its 105 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×#16861135 | C2 | semidirect |
| 3. C4×C22⋊Dic127 | C2 | semidirect |
| 4. #407×C127 | C2 | semidirect |
| 8. C2×#14523248 | C4 | semidirect |
| 10. C22×Dic254 | C4 | semidirect |
| 11. C22×D508 | C4 | semidirect |
| 15. C2×C4×Dic127 | C22 | semidirect |
| 19. C2×M16×C127 | C22 | semidirect |
| 61. Dic254 | C22⋊C4 | semidirect |
| 64. D508 | C22⋊C4 | semidirect |
| 99. C22×C127 | #104 | semidirect |
| 120. C127 | #1789 | semidirect |
| 123. #407 | D127 | semidirect |
| 135. C2×M16 | C2×D127 | semidirect |
| 223. C22 | #16861135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523248 | 2 |
| C2×#16861135 | 2 |
| C4×C22⋊Dic127 | 2 |
| #407×C127 | 2 |
| #1789 | 127 |