Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
248 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 105 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. Q8⋊(C127⋊C8) | C2 | semidirect |
| 46. Q8×C127 | M16 | semidirect |
| 79. C127 | #1487 | semidirect |
| 123. Q8 | #14523232 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549929 | 2 |
| #22549900 | 2 |
| Q8⋊(C127⋊C8) | 2 |
| C2×C4×Q8×C127 | 2 |
| #1487 | 127 |