Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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. #22553862 | C2 | semidirect |
| 2. #22553625 | C2 | semidirect |
| 3. #22553592 | C2 | semidirect |
| 4. #22553507 | C2 | semidirect |
| 5. #22553446 | C2 | semidirect |
| 6. C4×#14523498 | C2 | semidirect |
| 7. #22553365 | C2 | semidirect |
| 8. C2×C4×D4×C131 | C2 | semidirect |
| 11. #16862246 | C22 | semidirect |
| 12. #16862243 | C22 | semidirect |
| 17. C4×D524 | C22 | semidirect |
| 18. #16862179 | C22 | semidirect |
| 19. C4⋊(C131⋊C8) | C22 | semidirect |
| 21. #16862166 | C22 | semidirect |
| 23. C4×C131⋊C8 | C22 | semidirect |
| 81. D4×C131 | #41 | semidirect |
| 88. C2×C4×C131 | D8 | semidirect |
| 120. C131 | #3100 | semidirect |
| 123. C2×C4×D4 | D131 | semidirect |
| 199. D4 | #14523513 | semidirect |
| 208. C2×C4 | #14523498 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553862 | 2 |
| #22553625 | 2 |
| #22553592 | 2 |
| #22553507 | 2 |
| #22553446 | 2 |
| C4×#14523498 | 2 |
| #22553365 | 2 |
| C2×C4×D4×C131 | 2 |
| #3100 | 131 |