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. #22553967 | C2 | semidirect |
| 2. #22553947 | C2 | semidirect |
| 3. #22553658 | C2 | semidirect |
| 4. #22553624 | C2 | semidirect |
| 5. #22553593 | C2 | semidirect |
| 6. #22553545 | C2 | semidirect |
| 7. #22553444 | C2 | semidirect |
| 8. C4×#14523498 | C2 | semidirect |
| 9. #22553377 | C2 | semidirect |
| 10. #102×D131 | C2 | semidirect |
| 11. #459×C131 | C2 | semidirect |
| 16. C2×C8×D131 | C22 | semidirect |
| 17. #16862246 | C22 | semidirect |
| 22. #16862217 | C22 | semidirect |
| 26. C4⋊C4×D131 | C22 | semidirect |
| 27. #16862180 | C22 | semidirect |
| 28. #16862179 | C22 | semidirect |
| 30. #16862167 | C22 | semidirect |
| 31. #16862167 | C22 | semidirect |
| 32. #16862167 | C22 | semidirect |
| 34. (C2×D131)⋊C8 | C22 | semidirect |
| 35. C4×C131⋊C8 | C22 | semidirect |
| 36. C2×D8×C131 | C22 | semidirect |
| 38. C4×D4×C131 | C22 | semidirect |
| 39. C4⋊C8×C131 | C22 | semidirect |
| 40. #102×C131 | C22 | semidirect |
| 85. D524 | D8 | semidirect |
| 86. D524 | #41 | semidirect |
| 142. C131 | #3294 | semidirect |
| 150. #459 | D131 | semidirect |
| 159. C2×D8 | C2×D131 | semidirect |
| 171. C4×D4 | C2×D131 | semidirect |
| 175. C4⋊C8 | C2×D131 | semidirect |
| 181. #102 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553967 | 2 |
| #22553947 | 2 |
| #22553658 | 2 |
| #22553624 | 2 |
| #22553593 | 2 |
| #22553545 | 2 |
| #22553444 | 2 |
| C4×#14523498 | 2 |
| #22553377 | 2 |
| #102×D131 | 2 |
| #459×C131 | 2 |
| #3294 | 131 |