Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1008 conjugacy classes of subgroups; only the 269 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 269 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×#14523232 | C2 | semidirect |
| 3. #22549880 | C2 | direct (N × H) |
| 4. C2×#16861129 | C2 | semidirect |
| 5. C2×#117×C127 | C2 | semidirect |
| 10. C22×D508 | C4 | semidirect |
| 14. C2×#14523232 | C22 | semidirect |
| 15. C22×C127⋊C8 | C22 | semidirect |
| 16. #16861129 | C22 | semidirect |
| 19. #117×C127 | C22 | semidirect |
| 20. C2×C4⋊C4×C127 | C22 | semidirect |
| 34. C2×D508 | C2×C4 | semidirect |
| 38. C2×C127⋊C8 | C23 | semidirect |
| 48. C4⋊C4×C127 | C23 | semidirect |
| 93. C2×C127 | #418 | semidirect |
| 98. C127 | C2×#418 | semidirect |
| 101. C2×#117 | D127 | semidirect |
| 116. #117 | C2×D127 | semidirect |
| 117. C2×C4⋊C4 | C2×D127 | semidirect |
| 146. C4⋊C4 | C22×D127 | semidirect |
| 192. C2 | #22549880 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D508 | 2 |
| C22×#14523232 | 2 |
| #22549880 | 2 |
| C2×#16861129 | 2 |
| C2×#117×C127 | 2 |
| C2×#418 | 127 |