Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1660 conjugacy classes of subgroups; only the 1063 normal subgroups are shown.
This group has 1660 conjugacy classes of subgroups — too many to draw. Only its 1063 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. #22550359 | C2 | semidirect |
| 2. #22550351 | C2 | semidirect |
| 3. #41×Dic127 | C2 | semidirect |
| 4. C2×D4×Dic127 | C2 | semidirect |
| 6. C23×Dic127 | C22 | semidirect |
| 7. Q8×Dic127 | C22 | semidirect |
| 8. Q8×Dic127 | C22 | semidirect |
| 9. D4×Dic127 | C22 | semidirect |
| 10. D4×Dic127 | C22 | semidirect |
| 11. D4×Dic127 | C22 | semidirect |
| 12. #16861168 | C22 | semidirect |
| 13. C2×C4⋊Dic127 | C22 | semidirect |
| 14. C2×C22⋊Dic127 | C22 | semidirect |
| 15. C2×C4×Dic127 | C22 | semidirect |
| 16. H(5,𝔽2)×C127 | C4 | semidirect |
| 29. #41×C127 | C2×C4 | semidirect |
| 31. C2×D4×C127 | C2×C4 | semidirect |
| 42. C23×C127 | C22×C4 | semidirect |
| 44. Q8×C127 | C22×C4 | semidirect |
| 45. D4×C127 | C22×C4 | semidirect |
| 46. C2×C4×C127 | C22×C4 | semidirect |
| 56. Dic127 | H(5,𝔽2) | direct (N × H) |
| 62. C127 | C4×H(5,𝔽2) | semidirect |
| 68. H(5,𝔽2) | Dic127 | direct (N × H) |
| 82. #41 | C2×Dic127 | semidirect |
| 84. C2×D4 | C2×Dic127 | semidirect |
| 98. C23 | C22×Dic127 | semidirect |
| 100. Q8 | C22×Dic127 | semidirect |
| 101. D4 | C22×Dic127 | semidirect |
| 108. C2×C4 | C22×Dic127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550359 | 2 |
| #22550351 | 2 |
| #41×Dic127 | 2 |
| C2×D4×Dic127 | 2 |
| C2×H(5,𝔽2)×C127 | 2 |
| C4×H(5,𝔽2) | 127 |