Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
368 conjugacy classes of subgroups; only the 211 normal subgroups are shown.
This group has 368 conjugacy classes of subgroups — too many to draw. Only its 211 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. #22550294 | C2 | semidirect |
| 3. #22550293 | C2 | semidirect |
| 4. #22550292 | C2 | semidirect |
| 5. M32×D127 | C2 | semidirect |
| 6. C2×C16×D127 | C2 | semidirect |
| 7. #504×C127 | C2 | semidirect |
| 14. #16861149 | C22 | semidirect |
| 15. #16861148 | C22 | semidirect |
| 16. C2×C127⋊C16 | C22 | semidirect |
| 19. C16×D127 | C22 | semidirect |
| 20. C16×D127 | C22 | semidirect |
| 22. M32×C127 | C22 | semidirect |
| 23. C2×C16×C127 | C22 | semidirect |
| 71. D127 | #504 | direct (N × H) |
| 73. C127 | C2×#504 | semidirect |
| 78. #504 | D127 | direct (N × H) |
| 90. M32 | C2×D127 | semidirect |
| 96. C2×C16 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #131×D127 | 2 |
| #22550294 | 2 |
| #22550293 | 2 |
| #22550292 | 2 |
| M32×D127 | 2 |
| C2×C16×D127 | 2 |
| #504×C127 | 2 |
| C2×#504 | 127 |