Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
572 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 137 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×#16862278 | C2 | semidirect |
| 2. C2×#16862273 | C2 | semidirect |
| 3. #22553863 | C2 | semidirect |
| 4. #124×D131 | C2 | semidirect |
| 5. #22553704 | C2 | semidirect |
| 6. #22553702 | C2 | semidirect |
| 7. #22553701 | C2 | semidirect |
| 8. #22553697 | C2 | semidirect |
| 9. #22553693 | C2 | semidirect |
| 10. #22553264 | C2 | semidirect |
| 11. #497×C131 | C2 | semidirect |
| 17. C2×#14523503 | C22 | semidirect |
| 18. C2×#14523502 | C22 | semidirect |
| 20. C2×#14523500 | C22 | semidirect |
| 24. #16862243 | C22 | semidirect |
| 26. #16862235 | C22 | semidirect |
| 34. #16862157 | C22 | semidirect |
| 35. C8×Dic131 | C22 | semidirect |
| 36. C2×Q16×C131 | C22 | semidirect |
| 38. C4⋊Q8×C131 | C22 | semidirect |
| 40. #97×C131 | C22 | semidirect |
| 63. #14523496 | D4 | semidirect |
| 134. C131 | #3153 | semidirect |
| 141. #497 | D131 | semidirect |
| 153. C2×Q16 | C2×D131 | semidirect |
| 161. C4⋊Q8 | C2×D131 | semidirect |
| 174. #97 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862278 | 2 |
| C2×#16862273 | 2 |
| #22553863 | 2 |
| #124×D131 | 2 |
| #22553704 | 2 |
| #22553702 | 2 |
| #22553701 | 2 |
| #22553697 | 2 |
| #22553693 | 2 |
| #22553264 | 2 |
| #497×C131 | 2 |
| #3153 | 131 |