Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
440 conjugacy classes of subgroups; only the 241 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 241 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. Q8×C127⋊C8 | C2 | semidirect |
| 3. C8×Dic254 | C2 | semidirect |
| 4. #22550000 | C2 | semidirect |
| 7. C8×Q8×C127 | C2 | semidirect |
| 25. Q8×D127 | C8 | direct (N × H) |
| 32. C8×D127 | Q8 | direct (N × H) |
| 44. Dic254 | C2×C8 | semidirect |
| 53. C127⋊C8 | C2×Q8 | semidirect |
| 54. Q8×C127 | C2×C8 | semidirect |
| 59. C8×C127 | C2×Q8 | semidirect |
| 74. D127 | C8×Q8 | direct (N × H) |
| 76. C127 | C2×C8×Q8 | semidirect |
| 81. C8×Q8 | D127 | direct (N × H) |
| 121. Q8 | C8×D127 | direct (N × H) |
| 135. C8 | Q8×D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×Q8×D127 | 2 |
| Q8×C127⋊C8 | 2 |
| C8×Dic254 | 2 |
| #22550000 | 2 |
| C4⋊C8×D127 | 2 |
| C4×C8×D127 | 2 |
| C8×Q8×C127 | 2 |
| C2×C8×Q8 | 127 |