Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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×#14523235 | C2 | semidirect |
| 3. #22550026 | C2 | direct (N × H) |
| 4. C2×#16861129 | C2 | semidirect |
| 5. C2×C22⋊(C127⋊C8) | C2 | semidirect |
| 6. C2×C22⋊Q8×C127 | C2 | semidirect |
| 14. C2×#14523235 | C22 | semidirect |
| 15. C22×C127⋊C8 | C22 | semidirect |
| 16. #16861129 | C22 | semidirect |
| 17. C22⋊(C127⋊C8) | C22 | semidirect |
| 18. C22×Q8×C127 | C22 | semidirect |
| 21. C22⋊Q8×C127 | C22 | semidirect |
| 23. C2×C4⋊C4×C127 | C22 | semidirect |
| 40. C2×C127⋊C8 | C23 | semidirect |
| 44. C2×Q8×C127 | C23 | semidirect |
| 54. C4⋊C4×C127 | C23 | semidirect |
| 71. C23×C127 | SD16 | semidirect |
| 92. C22×C127 | C2×SD16 | semidirect |
| 106. C2×C127 | #450 | semidirect |
| 112. C127 | C2×#450 | semidirect |
| 115. C2×C22⋊Q8 | D127 | semidirect |
| 120. C22×Q8 | C2×D127 | semidirect |
| 131. C22⋊Q8 | C2×D127 | semidirect |
| 133. C2×C4⋊C4 | C2×D127 | semidirect |
| 145. C2×Q8 | C22×D127 | semidirect |
| 166. C4⋊C4 | C22×D127 | semidirect |
| 178. C23 | #14523235 | semidirect |
| 209. C22 | C2×#14523235 | semidirect |
| 219. C2 | #22550026 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D508 | 2 |
| C22×#14523235 | 2 |
| #22550026 | 2 |
| C2×#16861129 | 2 |
| C2×C22⋊(C127⋊C8) | 2 |
| C2×C22⋊Q8×C127 | 2 |
| C2×#450 | 127 |