Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
1260 conjugacy classes of subgroups; only the 485 normal subgroups are shown.
This group has 1260 conjugacy classes of subgroups — too many to draw. Only its 485 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. #22550482 | C2 | direct (N × H) |
| 2. C2×#16861206 | C2 | semidirect |
| 3. C2×#16861194 | C2 | semidirect |
| 4. C2×#16861184 | C2 | semidirect |
| 5. C2×#16861184 | C2 | semidirect |
| 6. C2×#16861171 | C2 | semidirect |
| 7. C2×#16861166 | C2 | semidirect |
| 8. C2×#125×C127 | C2 | semidirect |
| 14. #16861206 | C22 | semidirect |
| 15. #16861194 | C22 | semidirect |
| 16. #16861184 | C22 | semidirect |
| 17. #16861184 | C22 | semidirect |
| 18. #16861171 | C22 | semidirect |
| 19. #16861166 | C22 | semidirect |
| 25. #125×C127 | C22 | semidirect |
| 92. C2×C127 | #540 | semidirect |
| 98. C127 | C2×#540 | semidirect |
| 101. C2×#125 | D127 | semidirect |
| 113. #125 | C2×D127 | semidirect |
| 192. C2 | #22550482 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550482 | 2 |
| C2×#16861206 | 2 |
| C2×#16861194 | 2 |
| C2×#16861184 | 2 |
| C2×#16861171 | 2 |
| C2×#16861166 | 2 |
| C2×#125×C127 | 2 |
| C2×#540 | 127 |