Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
412 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862238 | C2 | semidirect |
| 3. #22553667 | C2 | direct (N × H) |
| 4. C2×#16862171 | C2 | semidirect |
| 6. C2×C4×C8×C131 | C2 | semidirect |
| 10. #16862238 | C22 | semidirect |
| 16. #16862171 | C22 | semidirect |
| 20. C4×C8×C131 | C22 | semidirect |
| 69. C2×C131 | #488 | semidirect |
| 73. C131 | C2×#488 | semidirect |
| 80. C2×C4×C8 | D131 | semidirect |
| 94. C4×C8 | C2×D131 | semidirect |
| 144. C2 | #22553667 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862238 | 2 |
| C2×#16862234 | 2 |
| #22553667 | 2 |
| C2×#16862171 | 2 |
| C2×#16862168 | 2 |
| C2×C4×C8×C131 | 2 |
| C2×#488 | 131 |