Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
656 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×SD16×D127 | C2 | semidirect |
| 2. C4⋊Q8×D127 | C2 | semidirect |
| 4. #22550250 | C2 | semidirect |
| 5. #22550249 | C2 | semidirect |
| 6. #22550248 | C2 | semidirect |
| 7. #22550247 | C2 | semidirect |
| 8. C4×C8×D127 | C2 | semidirect |
| 9. #492×C127 | C2 | semidirect |
| 13. C2×#14523237 | C22 | semidirect |
| 14. C2×#14523236 | C22 | semidirect |
| 15. C2×#14523235 | C22 | semidirect |
| 18. #16861209 | C22 | semidirect |
| 20. #16861207 | C22 | semidirect |
| 26. C4×C127⋊C8 | C22 | semidirect |
| 27. C8×Dic127 | C22 | semidirect |
| 28. C2×SD16×C127 | C22 | semidirect |
| 29. C4⋊Q8×C127 | C22 | semidirect |
| 31. C4×C8×C127 | C22 | semidirect |
| 49. C8×D127 | D4 | semidirect |
| 75. C4×D127 | SD16 | semidirect |
| 77. C127⋊C8 | C2×D4 | semidirect |
| 85. C8×C127 | C2×D4 | semidirect |
| 95. C4×C127 | C2×SD16 | semidirect |
| 99. Dic127 | C2×SD16 | semidirect |
| 104. D127 | #492 | direct (N × H) |
| 106. C127 | C2×#492 | semidirect |
| 114. #492 | D127 | direct (N × H) |
| 123. C2×SD16 | C2×D127 | semidirect |
| 128. C4⋊Q8 | C2×D127 | semidirect |
| 137. C4×C8 | C2×D127 | semidirect |
| 191. C8 | D4×D127 | semidirect |
| 204. C4 | SD16×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×D127 | 2 |
| C4⋊Q8×D127 | 2 |
| #127×D127 | 2 |
| #22550250 | 2 |
| #22550249 | 2 |
| #22550248 | 2 |
| #22550247 | 2 |
| C4×C8×D127 | 2 |
| #492×C127 | 2 |
| C2×#492 | 127 |