Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
280 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 280 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 |
|---|---|---|
| 4. #22549608 | C2 | semidirect |
| 5. Q8⋊(C127⋊C8) | C2 | semidirect |
| 6. #22549606 | C2 | semidirect |
| 7. Q8⋊C8×C127 | C2 | semidirect |
| 30. Q8×D127 | C8 | semidirect |
| 61. Dic254 | C2×C8 | semidirect |
| 77. Q8×C127 | C2×C8 | semidirect |
| 104. D127 | Q8⋊C8 | direct (N × H) |
| 106. C127 | C2×Q8⋊C8 | semidirect |
| 113. Q8⋊C8 | D127 | direct (N × H) |
| 169. Q8 | C8×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D127 | 2 |
| C4⋊C8×D127 | 2 |
| C4×C8×D127 | 2 |
| #22549608 | 2 |
| Q8⋊(C127⋊C8) | 2 |
| #22549606 | 2 |
| Q8⋊C8×C127 | 2 |
| C2×Q8⋊C8 | 127 |