Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1736 conjugacy classes of subgroups; only the 581 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 581 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. #22550548 | C2 | direct (N × H) |
| 3. C2×#16861206 | C2 | semidirect |
| 4. C2×#16861184 | C2 | semidirect |
| 5. C2×C4×D508 | C2 | semidirect |
| 6. C2×C4×Q8×C127 | C2 | semidirect |
| 8. C2×#14523249 | C22 | semidirect |
| 13. #16861206 | C22 | semidirect |
| 14. #16861184 | C22 | semidirect |
| 15. C4×D508 | C22 | semidirect |
| 19. C4×Q8×C127 | C22 | semidirect |
| 35. C2×Q8×C127 | D4 | semidirect |
| 53. Q8×C127 | C2×D4 | semidirect |
| 56. C2×C4×C127 | #41 | semidirect |
| 70. C4×C127 | C2×#41 | semidirect |
| 72. C2×C127 | #550 | semidirect |
| 78. C127 | C2×#550 | semidirect |
| 83. C2×C4×Q8 | D127 | semidirect |
| 94. C4×Q8 | C2×D127 | semidirect |
| 102. C2×Q8 | D508 | semidirect |
| 125. Q8 | C2×D508 | semidirect |
| 134. C2×C4 | #14523249 | semidirect |
| 149. C4 | C2×#14523249 | semidirect |
| 151. C2 | #22550548 | 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 |
| #22550548 | 2 |
| C2×#16861206 | 2 |
| C2×#16861184 | 2 |
| C2×C4×D508 | 2 |
| C2×C4×Q8×C127 | 2 |
| C2×#550 | 127 |