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. #22550480 | C2 | direct (N × H) |
| 2. C2×#16861201 | C2 | semidirect |
| 3. C2×#16861190 | C2 | semidirect |
| 4. C2×#16861181 | C2 | semidirect |
| 5. C2×#16861180 | C2 | semidirect |
| 6. C2×D4×Dic127 | C2 | semidirect |
| 7. C2×#16861166 | C2 | semidirect |
| 8. C2×#127×C127 | C2 | semidirect |
| 12. #16861201 | C22 | semidirect |
| 13. #16861190 | C22 | semidirect |
| 14. #16861181 | C22 | semidirect |
| 15. #16861180 | C22 | semidirect |
| 16. D4×Dic127 | C22 | semidirect |
| 17. #16861166 | C22 | semidirect |
| 27. #127×C127 | C22 | semidirect |
| 93. C2×C127 | #540 | semidirect |
| 98. C127 | C2×#540 | semidirect |
| 100. C2×#127 | D127 | semidirect |
| 112. #127 | C2×D127 | semidirect |
| 192. C2 | #22550480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22550480 | 2 |
| C2×#16861201 | 2 |
| C2×#16861190 | 2 |
| C2×#16861181 | 2 |
| C2×#16861180 | 2 |
| C2×D4×Dic127 | 2 |
| C2×#16861166 | 2 |
| C2×#127×C127 | 2 |
| C2×#540 | 127 |