Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
512 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 512 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×C4⋊C4×D127 | C2 | semidirect |
| 3. #22550191 | C2 | direct (N × H) |
| 4. C2×#16861142 | C2 | semidirect |
| 5. C2×#16861131 | C2 | semidirect |
| 6. C2×#16861129 | C2 | semidirect |
| 7. C2×(C2×D127)⋊C8 | C2 | semidirect |
| 8. C2×#107×C127 | C2 | semidirect |
| 19. C4⋊C4×D127 | C22 | semidirect |
| 21. #16861142 | C22 | semidirect |
| 22. #16861131 | C22 | semidirect |
| 23. #16861129 | C22 | semidirect |
| 24. (C2×D127)⋊C8 | C22 | semidirect |
| 28. #107×C127 | C22 | semidirect |
| 110. C2×C127 | #480 | semidirect |
| 117. C127 | C2×#480 | semidirect |
| 122. C2×#107 | D127 | semidirect |
| 142. #107 | C2×D127 | semidirect |
| 229. C2 | #22550191 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861184 | 2 |
| C2×C4⋊C4×D127 | 2 |
| #22550191 | 2 |
| C2×#16861142 | 2 |
| C2×#16861131 | 2 |
| C2×#16861129 | 2 |
| C2×(C2×D127)⋊C8 | 2 |
| C2×#107×C127 | 2 |
| C2×#480 | 127 |