Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
136 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 136 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
|---|---|---|
| 55. C127 | #1290 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549933 | 2 |
| C2×C4⋊(C127⋊C8) | 2 |
| #432×C127 | 2 |
| #1290 | 127 |