Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
648 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 648 conjugacy classes of subgroups — too many to draw. Only its 173 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 |
|---|---|---|
| 2. #22553192 | C2 | semidirect |
| 3. #22553191 | C2 | semidirect |
| 4. #22553190 | C2 | semidirect |
| 5. #22553189 | C2 | semidirect |
| 6. #22553188 | C2 | semidirect |
| 7. #22553188 | C2 | semidirect |
| 8. #22553179 | C2 | semidirect |
| 9. #386×C131 | C2 | semidirect |
| 15. #16862242 | C4 | semidirect |
| 35. C2×D524 | C2×C4 | semidirect |
| 40. C2×C22⋊D131 | C2×C4 | semidirect |
| 41. C2×C22⋊D131 | C2×C4 | semidirect |
| 55. C4×Dic131 | C2×C4 | semidirect |
| 60. C2×D4×C131 | C2×C4 | semidirect |
| 147. C131 | #2380 | semidirect |
| 156. #386 | D131 | semidirect |
| 194. C2×D4 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862242 | 2 |
| #22553192 | 2 |
| #22553191 | 2 |
| #22553190 | 2 |
| #22553189 | 2 |
| #22553188 | 2 |
| #22553179 | 2 |
| #386×C131 | 2 |
| #2380 | 131 |