Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
494 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 123 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. #22553947 | C2 | semidirect |
| 3. #22553624 | C2 | semidirect |
| 4. #22553589 | C2 | semidirect |
| 5. #22553547 | C2 | semidirect |
| 6. #22553504 | C2 | semidirect |
| 7. #22553447 | C2 | semidirect |
| 8. C4×D1048 | C2 | semidirect |
| 9. C8×D524 | C2 | semidirect |
| 10. #102×D131 | C2 | semidirect |
| 11. #486×C131 | C2 | semidirect |
| 16. C2×#14523498 | C22 | semidirect |
| 17. C2×C8×D131 | C22 | semidirect |
| 20. #16862221 | C22 | semidirect |
| 26. C4×D524 | C22 | semidirect |
| 27. C4⋊C4×D131 | C22 | semidirect |
| 28. #16862180 | C22 | semidirect |
| 29. #16862179 | C22 | semidirect |
| 30. C4⋊(C131⋊C8) | C22 | semidirect |
| 32. #16862168 | C22 | semidirect |
| 33. #16862167 | C22 | semidirect |
| 35. (C2×D131)⋊C8 | C22 | semidirect |
| 36. C4⋊Q8×C131 | C22 | semidirect |
| 38. #102×C131 | C22 | semidirect |
| 39. #102×C131 | C22 | semidirect |
| 40. C4×C8×C131 | C22 | semidirect |
| 88. D524 | D8 | semidirect |
| 89. D524 | #41 | semidirect |
| 142. C131 | #3294 | semidirect |
| 146. #486 | D131 | semidirect |
| 161. C4⋊Q8 | C2×D131 | semidirect |
| 180. #102 | C2×D131 | semidirect |
| 181. #102 | C2×D131 | semidirect |
| 183. C4×C8 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553965 | 2 |
| #22553947 | 2 |
| #22553624 | 2 |
| #22553589 | 2 |
| #22553547 | 2 |
| #22553504 | 2 |
| #22553447 | 2 |
| C4×D1048 | 2 |
| C8×D524 | 2 |
| #102×D131 | 2 |
| #486×C131 | 2 |
| #3294 | 131 |