Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
488 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16861234 | C2 | semidirect |
| 2. C22×D1016 | C2 | semidirect |
| 3. #22550146 | C2 | direct (N × H) |
| 4. C2×#16861145 | C2 | semidirect |
| 5. C2×#16861125 | C2 | semidirect |
| 6. C2×#131×C127 | C2 | semidirect |
| 9. #16861234 | C22 | semidirect |
| 14. C2×D1016 | C22 | semidirect |
| 17. #16861145 | C22 | semidirect |
| 18. #16861125 | C22 | semidirect |
| 21. #131×C127 | C22 | semidirect |
| 105. C2×C127 | #472 | semidirect |
| 109. C127 | C2×#472 | semidirect |
| 112. C2×#131 | D127 | semidirect |
| 127. #131 | C2×D127 | semidirect |
| 215. C2 | #22550146 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861234 | 2 |
| C22×D1016 | 2 |
| #22550146 | 2 |
| C2×#16861145 | 2 |
| C2×#16861125 | 2 |
| C2×#131×C127 | 2 |
| C2×#472 | 127 |