Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
820 conjugacy classes of subgroups; only the 245 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 245 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. C22×C4⋊Dic127 | C2 | semidirect |
| 3. #22549801 | C2 | direct (N × H) |
| 4. C2×C127⋊#95 | C2 | semidirect |
| 5. C2×C127⋊#95 | C2 | semidirect |
| 10. C2×C4⋊Dic127 | C22 | semidirect |
| 13. C127⋊#95 | C22 | semidirect |
| 14. C127⋊#95 | C22 | semidirect |
| 95. C2×C127 | #397 | semidirect |
| 102. C127 | C2×#397 | semidirect |
| 197. C2 | #22549801 | 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×C22⋊Dic127 | 2 |
| #22549801 | 2 |
| C2×C127⋊#95 | 2 |
| C22×C22⋊C4×C127 | 2 |
| C2×#397 | 127 |