Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
224 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 81 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. C2×#16861149 | C2 | semidirect |
| 3. #22549685 | C2 | semidirect |
| 4. #427×C127 | C2 | semidirect |
| 8. #16861231 | C4 | semidirect |
| 10. C2×Dic508 | C4 | semidirect |
| 12. C2×D1016 | C4 | semidirect |
| 14. #16861149 | C22 | semidirect |
| 19. #106×C127 | C22 | semidirect |
| 85. C127 | #2145 | semidirect |
| 88. #427 | D127 | semidirect |
| 104. #106 | C2×D127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16861231 | 2 |
| C2×#16861149 | 2 |
| #22549685 | 2 |
| #427×C127 | 2 |
| #2145 | 127 |