Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
224 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 77 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. M32×D127 | C2 | semidirect |
| 3. C2×C16×D127 | C2 | semidirect |
| 4. #22549661 | C2 | semidirect |
| 5. #22549660 | C2 | semidirect |
| 6. #22549659 | C2 | semidirect |
| 7. #350×C127 | C2 | semidirect |
| 18. #16861149 | C22 | semidirect |
| 20. C2×C127⋊C16 | C22 | semidirect |
| 25. M32×C127 | C22 | semidirect |
| 26. C2×C16×C127 | C22 | semidirect |
| 107. D127 | #350 | direct (N × H) |
| 109. C127 | C2×#350 | semidirect |
| 116. #350 | D127 | direct (N × H) |
| 130. M32 | C2×D127 | semidirect |
| 135. 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 |
| M32×D127 | 2 |
| C2×C16×D127 | 2 |
| #22549661 | 2 |
| #22549660 | 2 |
| #22549659 | 2 |
| #350×C127 | 2 |
| C2×#350 | 127 |