Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
166 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
|---|---|---|
| 3. C4⋊(C127⋊C16) | C2 | semidirect |
| 4. #22549680 | C2 | semidirect |
| 5. #494×C127 | C2 | semidirect |
| 52. C4×C127 | SD32 | semidirect |
| 61. C127 | #2208 | semidirect |
| 63. #494 | D127 | semidirect |
| 114. C4 | #16861152 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861152 | 2 |
| C4×D1016 | 2 |
| C4⋊(C127⋊C16) | 2 |
| #22549680 | 2 |
| #494×C127 | 2 |
| #2208 | 127 |