Finite Group DatabasebetaFinite Group DatabasebetaOrder 16064.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 111 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×#16860810 | C2 | semidirect |
| 2. #22548735 | C2 | direct (N × H) |
| 3. C2×#16860800 | C2 | semidirect |
| 4. C2×#16860798 | C2 | semidirect |
| 5. C2×#16860797 | C2 | semidirect |
| 6. C2×#16860795 | C2 | semidirect |
| 7. C22×C251⋊C8 | C2 | semidirect |
| 8. C2×#41×C251 | C2 | semidirect |
| 10. #16860810 | C22 | semidirect |
| 15. #16860800 | C22 | semidirect |
| 16. #16860798 | C22 | semidirect |
| 17. #16860797 | C22 | semidirect |
| 18. #16860795 | C22 | semidirect |
| 21. C2×C251⋊C8 | C22 | semidirect |
| 23. #41×C251 | C22 | semidirect |
| 66. C2×C251 | #135 | semidirect |
| 69. C251 | C2×#135 | semidirect |
| 72. C2×#41 | D251 | semidirect |
| 82. #41 | C2×D251 | semidirect |
| 137. C2 | #22548735 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16860810 | 2 |
| #22548735 | 2 |
| C2×#16860800 | 2 |
| C2×#16860798 | 2 |
| C2×#16860797 | 2 |
| C2×#16860795 | 2 |
| C22×C251⋊C8 | 2 |
| C2×#41×C251 | 2 |
| C2×#135 | 251 |