Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
464 conjugacy classes of subgroups; only the 233 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 233 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 |
|---|---|---|
| 21. C4×Q8×C127 | C4 | semidirect |
| 87. C127 | #2356 | semidirect |
| 97. C4×Q8 | Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549783 | 2 |
| #22549762 | 2 |
| #22549744 | 2 |
| #22549742 | 2 |
| C4⋊C4×Dic127 | 2 |
| C4×C4⋊Dic127 | 2 |
| #22549722 | 2 |
| C2×C4×Q8×C127 | 2 |
| #2356 | 127 |