Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862276 | C2 | semidirect |
| 2. C2×#16862233 | C2 | semidirect |
| 3. #41×Dic131 | C2 | semidirect |
| 4. #22553532 | C2 | semidirect |
| 5. #22553525 | C2 | semidirect |
| 6. #22553335 | C2 | semidirect |
| 7. #22553322 | C2 | semidirect |
| 8. #22553317 | C2 | semidirect |
| 12. C2×#14523503 | C22 | semidirect |
| 13. C2×#14523501 | C22 | semidirect |
| 18. Q8×Dic131 | C22 | semidirect |
| 20. D4×Dic131 | C22 | semidirect |
| 26. Dic131⋊C8 | C22 | semidirect |
| 27. #16862171 | C22 | semidirect |
| 125. C131 | #3040 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862276 | 2 |
| C2×#16862233 | 2 |
| #41×Dic131 | 2 |
| #22553532 | 2 |
| #22553525 | 2 |
| #22553335 | 2 |
| #22553322 | 2 |
| #22553317 | 2 |
| C2×AGL(1,ℤ/8)×C131 | 2 |
| #3040 | 131 |