Finite Group DatabasebetaFinite Group DatabasebetaOrder 16256.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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×#16861231 | C2 | semidirect |
| 2. C2×#16861228 | C2 | semidirect |
| 3. #22550544 | C2 | semidirect |
| 4. #22550251 | C2 | semidirect |
| 5. #22550113 | C2 | semidirect |
| 6. #22550075 | C2 | semidirect |
| 7. #22550022 | C2 | semidirect |
| 8. #22550019 | C2 | semidirect |
| 9. #22549970 | C2 | semidirect |
| 10. C8×C22⋊D127 | C2 | semidirect |
| 11. #466×C127 | C2 | semidirect |
| 56. Dic508 | D4 | semidirect |
| 134. Dic127 | #135 | semidirect |
| 143. C127 | #3287 | semidirect |
| 149. #466 | 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×#16861228 | 2 |
| #22550544 | 2 |
| #22550251 | 2 |
| #22550113 | 2 |
| #22550075 | 2 |
| #22550022 | 2 |
| #22550019 | 2 |
| #22549970 | 2 |
| C8×C22⋊D127 | 2 |
| #466×C127 | 2 |
| #3287 | 127 |