Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
312 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 1. #22549929 | C2 | semidirect |
| 2. #22549600 | C2 | semidirect |
| 18. C2×D4×C127 | C8 | semidirect |
| 72. C127 | #1460 | semidirect |
| 89. C2×D4 | C127⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22549929 | 2 |
| #22549600 | 2 |
| C2×C4×D4×C127 | 2 |
| #1460 | 127 |