Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
668 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 668 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. C22×#14523235 | C2 | semidirect |
| 2. C22×D1016 | C2 | semidirect |
| 3. C22×#14523233 | C2 | semidirect |
| 4. C2×#16861205 | C2 | semidirect |
| 5. C2×#16861198 | C2 | semidirect |
| 6. #22550262 | C2 | direct (N × H) |
| 7. C2×#16861119 | C2 | semidirect |
| 8. C22×SD16×C127 | C2 | semidirect |
| 13. C2×#14523235 | C22 | semidirect |
| 15. C2×D1016 | C22 | semidirect |
| 17. C2×#14523233 | C22 | semidirect |
| 20. #16861205 | C22 | semidirect |
| 22. #16861198 | C22 | semidirect |
| 25. #16861119 | C22 | semidirect |
| 29. C2×SD16×C127 | C22 | semidirect |
| 47. C2×C127⋊C8 | D4 | semidirect |
| 64. C2×C8×C127 | D4 | semidirect |
| 81. C127⋊C8 | C2×D4 | semidirect |
| 98. C8×C127 | C2×D4 | semidirect |
| 117. C2×C127 | #496 | semidirect |
| 123. C127 | C2×#496 | semidirect |
| 125. C22×SD16 | D127 | semidirect |
| 140. C2×SD16 | C2×D127 | semidirect |
| 184. C2×C8 | C22⋊D127 | semidirect |
| 221. C8 | C2×C22⋊D127 | semidirect |
| 242. C2 | #22550262 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523235 | 2 |
| C22×D1016 | 2 |
| C22×#14523233 | 2 |
| C2×#16861205 | 2 |
| C2×#16861198 | 2 |
| #22550262 | 2 |
| C2×#16861119 | 2 |
| C22×SD16×C127 | 2 |
| C2×#496 | 127 |