Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
456 conjugacy classes of subgroups; only the 185 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 185 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×#16861215 | C2 | semidirect |
| 3. #22549999 | C2 | semidirect |
| 4. #22549994 | C2 | semidirect |
| 5. #22549925 | C2 | semidirect |
| 6. #22549894 | C2 | semidirect |
| 7. #405×C127 | C2 | semidirect |
| 9. #16861242 | C4 | semidirect |
| 10. #16861237 | C4 | semidirect |
| 14. #16861215 | C22 | semidirect |
| 15. #16861215 | C22 | semidirect |
| 19. #16861145 | C22 | semidirect |
| 20. #16861137 | C22 | semidirect |
| 24. #97×C127 | C22 | semidirect |
| 25. C4×C8×C127 | C22 | semidirect |
| 90. C127 | #2955 | semidirect |
| 97. #405 | D127 | semidirect |
| 114. #97 | C2×D127 | semidirect |
| 115. C4×C8 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550676 | 2 |
| C2×#16861215 | 2 |
| #22549999 | 2 |
| #22549994 | 2 |
| #22549925 | 2 |
| #22549894 | 2 |
| #405×C127 | 2 |
| #2955 | 127 |