Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
400 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16861152 | C2 | direct (N × H) |
| 3. C22×C127⋊C16 | C2 | semidirect |
| 4. C22×Q16×C127 | C2 | semidirect |
| 8. #16861152 | C22 | direct (N × H) |
| 9. C2×C127⋊C16 | C22 | semidirect |
| 12. C2×Q16×C127 | C22 | semidirect |
| 19. C127⋊C16 | C23 | semidirect |
| 25. Q16×C127 | C23 | semidirect |
| 40. C22×C127 | SD32 | semidirect |
| 47. C2×C127 | C2×SD32 | semidirect |
| 51. C127 | C22×SD32 | semidirect |
| 52. C22×Q16 | D127 | semidirect |
| 59. C2×Q16 | C2×D127 | semidirect |
| 73. Q16 | C22×D127 | semidirect |
| 93. C22 | #16861152 | direct (N × H) |
| 99. C2 | C2×#16861152 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1016 | 2 |
| C2×#16861152 | 2 |
| C22×C127⋊C16 | 2 |
| C22×Q16×C127 | 2 |
| C22×SD32 | 127 |