Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
494 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553965 | C2 | semidirect |
| 2. D4×D524 | C2 | semidirect |
| 3. #22553660 | C2 | semidirect |
| 4. #22553627 | C2 | semidirect |
| 5. #22553549 | C2 | semidirect |
| 6. #22553508 | C2 | semidirect |
| 7. #22553447 | C2 | semidirect |
| 8. C4×#14523498 | C2 | semidirect |
| 9. #22553377 | C2 | semidirect |
| 10. #102×D131 | C2 | semidirect |
| 11. #474×C131 | C2 | semidirect |
| 15. C2×D1048 | C22 | semidirect |
| 17. C2×C8×D131 | C22 | semidirect |
| 22. #16862221 | C22 | semidirect |
| 26. C4×D524 | C22 | semidirect |
| 27. C4⋊C4×D131 | C22 | semidirect |
| 28. #16862179 | C22 | semidirect |
| 29. #16862168 | C22 | semidirect |
| 31. #16862166 | C22 | semidirect |
| 32. #16862166 | C22 | semidirect |
| 33. #16862166 | C22 | semidirect |
| 34. (C2×D131)⋊C8 | C22 | semidirect |
| 35. C4×C131⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C131 | C22 | semidirect |
| 38. #107×C131 | C22 | semidirect |
| 39. C4⋊C8×C131 | C22 | semidirect |
| 92. D524 | D8 | semidirect |
| 105. D4×C131 | #41 | semidirect |
| 142. C131 | #3294 | semidirect |
| 148. #474 | D131 | semidirect |
| 161. C4⋊Q8 | C2×D131 | semidirect |
| 174. #107 | C2×D131 | semidirect |
| 175. C4⋊C8 | C2×D131 | semidirect |
| 240. D4 | #14523514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553965 | 2 |
| D4×D524 | 2 |
| #22553660 | 2 |
| #22553627 | 2 |
| #22553549 | 2 |
| #22553508 | 2 |
| #22553447 | 2 |
| C4×#14523498 | 2 |
| #22553377 | 2 |
| #102×D131 | 2 |
| #474×C131 | 2 |
| #3294 | 131 |