Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
912 conjugacy classes of subgroups; only the 389 normal subgroups are shown.
This group has 912 conjugacy classes of subgroups — too many to draw. Only its 389 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 |
|---|---|---|
| 2. C22⋊C4×Dic127 | C2 | semidirect |
| 3. C4×C22⋊Dic127 | C2 | semidirect |
| 6. C2×C22⋊Dic127 | C4 | semidirect |
| 9. C2×C4×Dic127 | C22 | semidirect |
| 10. C127⋊#95 | C22 | semidirect |
| 13. C2×C22⋊C4×C127 | C4 | semidirect |
| 16. C22×Dic127 | C2×C4 | semidirect |
| 18. C22⋊Dic127 | C2×C4 | semidirect |
| 19. C22⋊Dic127 | C2×C4 | semidirect |
| 27. C22×C4×C127 | C2×C4 | semidirect |
| 29. C22⋊C4×C127 | C2×C4 | semidirect |
| 37. C23×C127 | C42 | semidirect |
| 66. C127 | #2273 | semidirect |
| 77. C2×C22⋊C4 | Dic127 | semidirect |
| 90. C22×C4 | C2×Dic127 | semidirect |
| 94. C22⋊C4 | C2×Dic127 | semidirect |
| 100. C23 | C4×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic127 | 2 |
| C22⋊C4×Dic127 | 2 |
| C4×C22⋊Dic127 | 2 |
| C22×C22⋊C4×C127 | 2 |
| #2273 | 127 |