Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
712 conjugacy classes of subgroups; only the 349 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 349 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. #22549741 | C2 | direct (N × H) |
| 10. C2×C4×Dic127 | C4 | semidirect |
| 25. C4×Dic127 | C2×C4 | semidirect |
| 69. C2×C127 | #382 | semidirect |
| 76. C127 | C2×#382 | semidirect |
| 145. C2 | #22549741 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊Dic127 | 2 |
| C22×C4×Dic127 | 2 |
| #22549741 | 2 |
| C2×C127⋊#95 | 2 |
| C22×C4⋊C4×C127 | 2 |
| C2×#382 | 127 |