Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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×Q8×D127 | C2 | semidirect |
| 3. C22×#14523237 | C2 | semidirect |
| 4. C22×#14523236 | C2 | semidirect |
| 5. C22×#14523235 | C2 | semidirect |
| 6. C2×SD16×D127 | C2 | direct (N × H) |
| 7. C22×C8×D127 | C2 | semidirect |
| 8. C22×SD16×C127 | C2 | semidirect |
| 11. C22×Dic254 | C22 | semidirect |
| 13. C2×Q8×D127 | C22 | semidirect |
| 20. C2×#14523237 | C22 | semidirect |
| 21. C2×#14523236 | C22 | semidirect |
| 22. C2×#14523235 | C22 | semidirect |
| 23. SD16×D127 | C22 | direct (N × H) |
| 24. C22×C127⋊C8 | C22 | semidirect |
| 25. C2×C8×D127 | C22 | semidirect |
| 26. C22×Q8×C127 | C22 | semidirect |
| 28. C2×SD16×C127 | C22 | semidirect |
| 29. C22×C8×C127 | C22 | semidirect |
| 36. C2×Dic254 | C23 | semidirect |
| 38. Q8×D127 | C23 | semidirect |
| 49. #14523237 | C23 | semidirect |
| 50. #14523236 | C23 | semidirect |
| 51. #14523235 | C23 | semidirect |
| 52. C2×C127⋊C8 | C23 | semidirect |
| 53. C8×D127 | C23 | semidirect |
| 56. C2×Q8×C127 | C23 | semidirect |
| 61. SD16×C127 | C23 | semidirect |
| 62. C2×C8×C127 | C23 | semidirect |
| 67. C22×D127 | SD16 | direct (N × H) |
| 71. Dic254 | C24 | semidirect |
| 80. C127⋊C8 | C24 | semidirect |
| 85. Q8×C127 | C24 | semidirect |
| 91. C8×C127 | C24 | semidirect |
| 94. C22×C127 | C2×SD16 | semidirect |
| 99. C2×D127 | C2×SD16 | direct (N × H) |
| 107. C2×C127 | C22×SD16 | semidirect |
| 110. D127 | C22×SD16 | direct (N × H) |
| 112. C127 | C23×SD16 | semidirect |
| 119. C22×SD16 | D127 | direct (N × H) |
| 126. C22×Q8 | C2×D127 | semidirect |
| 138. C2×SD16 | C2×D127 | direct (N × H) |
| 141. C22×C8 | C2×D127 | semidirect |
| 153. C2×Q8 | C22×D127 | semidirect |
| 171. SD16 | C22×D127 | direct (N × H) |
| 174. C2×C8 | C22×D127 | semidirect |
| 188. Q8 | C23×D127 | semidirect |
| 203. C8 | C23×D127 | semidirect |
| 211. C22 | SD16×D127 | direct (N × H) |
| 221. C2 | C2×SD16×D127 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Q8×D127 | 2 |
| C22×D4×D127 | 2 |
| C22×#14523237 | 2 |
| C22×#14523236 | 2 |
| C22×#14523235 | 2 |
| C2×SD16×D127 | 2 |
| C22×C8×D127 | 2 |
| C22×SD16×C127 | 2 |
| C23×SD16 | 127 |