Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
552 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 221 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. C4×#14523235 | C2 | direct (N × H) |
| 4. C2×#16861140 | C2 | semidirect |
| 5. C2×#16861133 | C2 | semidirect |
| 7. C2×C4×C127⋊C8 | C2 | semidirect |
| 8. C2×C4×Q8×C127 | C2 | semidirect |
| 11. C2×#14523235 | C4 | direct (N × H) |
| 19. #16861140 | C22 | semidirect |
| 20. #16861133 | C22 | semidirect |
| 22. C4×C127⋊C8 | C22 | semidirect |
| 25. C4×Q8×C127 | C22 | semidirect |
| 38. #14523235 | C2×C4 | direct (N × H) |
| 40. C2×C127⋊C8 | C2×C4 | semidirect |
| 48. C2×Q8×C127 | C2×C4 | semidirect |
| 72. C127⋊C8 | C22×C4 | semidirect |
| 76. Q8×C127 | C22×C4 | semidirect |
| 82. C2×C4×C127 | SD16 | semidirect |
| 101. C4×C127 | C2×SD16 | semidirect |
| 105. C2×C127 | C4×SD16 | semidirect |
| 111. C127 | C2×C4×SD16 | semidirect |
| 113. C2×C4×Q8 | D127 | semidirect |
| 128. C4×Q8 | C2×D127 | semidirect |
| 144. C2×Q8 | C4×D127 | semidirect |
| 179. Q8 | C2×C4×D127 | semidirect |
| 191. C2×C4 | #14523235 | direct (N × H) |
| 213. C4 | C2×#14523235 | direct (N × H) |
| 217. C2 | C4×#14523235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523235 | 2 |
| C2×C4×D508 | 2 |
| C4×#14523235 | 2 |
| C2×#16861140 | 2 |
| C2×#16861133 | 2 |
| C2×#16861129 | 2 |
| C2×C4×C127⋊C8 | 2 |
| C2×C4×Q8×C127 | 2 |
| C2×C4×SD16 | 127 |