Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 573 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 |
|---|---|---|
| 1. C22×#14523249 | C2 | semidirect |
| 2. #22550545 | C2 | direct (N × H) |
| 3. C2×#16861205 | C2 | semidirect |
| 4. C2×#16861183 | C2 | semidirect |
| 5. C2×#16861180 | C2 | semidirect |
| 6. C2×Q8×Dic127 | C2 | semidirect |
| 7. C2×C4×C22⋊D127 | C2 | semidirect |
| 8. C22×#41×C127 | C2 | semidirect |
| 10. C2×#14523249 | C22 | semidirect |
| 15. #16861205 | C22 | semidirect |
| 16. #16861183 | C22 | semidirect |
| 17. #16861180 | C22 | semidirect |
| 18. Q8×Dic127 | C22 | semidirect |
| 19. C4×C22⋊D127 | C22 | semidirect |
| 26. C2×#41×C127 | C22 | semidirect |
| 50. C2×Q8×C127 | D4 | semidirect |
| 67. C2×Dic127 | #41 | semidirect |
| 77. Q8×C127 | C2×D4 | semidirect |
| 100. Dic127 | C2×#41 | semidirect |
| 102. C2×C127 | #550 | semidirect |
| 108. C127 | C2×#550 | semidirect |
| 110. C22×#41 | D127 | semidirect |
| 120. C2×#41 | C2×D127 | semidirect |
| 142. C2×Q8 | C22⋊D127 | semidirect |
| 175. Q8 | C2×C22⋊D127 | semidirect |
| 211. C2 | #22550545 | 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 |
| #22550545 | 2 |
| C2×#16861205 | 2 |
| C2×#16861183 | 2 |
| C2×#16861180 | 2 |
| C2×Q8×Dic127 | 2 |
| C2×C4×C22⋊D127 | 2 |
| C22×#41×C127 | 2 |
| C2×#550 | 127 |