Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
816 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 816 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. C22×#14523231 | C2 | semidirect |
| 3. C2×C4⋊C4×D127 | C2 | semidirect |
| 4. #22549876 | C2 | direct (N × H) |
| 5. C2×#16861133 | C2 | semidirect |
| 6. C2×#16861131 | C2 | semidirect |
| 7. C2×#16861129 | C2 | semidirect |
| 8. C2×#103×C127 | C2 | semidirect |
| 11. C2×#14523249 | C4 | semidirect |
| 19. C2×#14523231 | C22 | semidirect |
| 24. C4⋊C4×D127 | C22 | semidirect |
| 25. #16861133 | C22 | semidirect |
| 26. #16861131 | C22 | semidirect |
| 27. #16861129 | C22 | semidirect |
| 31. #103×C127 | C22 | semidirect |
| 36. #14523249 | C2×C4 | semidirect |
| 41. C2×D508 | C2×C4 | semidirect |
| 61. C2×Q8×C127 | C2×C4 | semidirect |
| 81. D508 | C22×C4 | semidirect |
| 95. Q8×C127 | C22×C4 | semidirect |
| 124. C2×C127 | #417 | semidirect |
| 131. C127 | C2×#417 | semidirect |
| 137. C2×#103 | D127 | semidirect |
| 160. #103 | C2×D127 | semidirect |
| 170. C2×Q8 | C4×D127 | semidirect |
| 212. Q8 | C2×C4×D127 | semidirect |
| 257. C2 | #22549876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523249 | 2 |
| C22×#14523231 | 2 |
| C2×C4⋊C4×D127 | 2 |
| #22549876 | 2 |
| C2×#16861133 | 2 |
| C2×#16861131 | 2 |
| C2×#16861129 | 2 |
| C2×#103×C127 | 2 |
| C2×#417 | 127 |