Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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×#16862271 | C2 | semidirect |
| 2. C2×#16862235 | C2 | semidirect |
| 3. #22553485 | C2 | direct (N × H) |
| 4. C2×#16862173 | C2 | semidirect |
| 5. C2×#16862165 | C2 | semidirect |
| 6. C2×2−1+4×C131 | C2 | semidirect |
| 9. #16862271 | C22 | semidirect |
| 14. #16862235 | C22 | semidirect |
| 17. #16862173 | C22 | semidirect |
| 18. #16862165 | C22 | semidirect |
| 21. 2−1+4×C131 | C22 | semidirect |
| 114. C2×C131 | #454 | semidirect |
| 117. C131 | C2×#454 | semidirect |
| 119. C2×2−1+4 | D131 | semidirect |
| 127. 2−1+4 | C2×D131 | semidirect |
| 233. C2 | #22553485 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C2×#16862235 | 2 |
| #22553485 | 2 |
| C2×#16862173 | 2 |
| C2×#16862165 | 2 |
| C2×2−1+4×C131 | 2 |
| C2×#454 | 131 |