Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
260 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16861149 | C2 | semidirect |
| 3. (C2×D127)⋊C16 | C2 | semidirect |
| 4. C2×M32×C127 | C2 | semidirect |
| 12. C2×C127⋊C16 | C22 | semidirect |
| 15. C2×C16×C127 | C22 | semidirect |
| 57. C2×D127 | M32 | semidirect |
| 67. C127 | #2112 | semidirect |
| 70. C2×M32 | D127 | semidirect |
| 82. C2×C16 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C8×D127 | 2 |
| C2×#16861149 | 2 |
| (C2×D127)⋊C16 | 2 |
| C2×M32×C127 | 2 |
| #2112 | 127 |