Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 181 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. C23×D524 | C2 | semidirect |
| 2. C22×#14523498 | C2 | semidirect |
| 3. #22553445 | C2 | direct (N × H) |
| 4. C2×#16862166 | C2 | semidirect |
| 5. C2×C22⋊(C131⋊C8) | C2 | semidirect |
| 6. C2×#121×C131 | C2 | semidirect |
| 12. C22×D524 | C22 | semidirect |
| 14. C2×#14523498 | C22 | semidirect |
| 15. C22×C131⋊C8 | C22 | semidirect |
| 16. #16862166 | C22 | semidirect |
| 17. C22⋊(C131⋊C8) | C22 | semidirect |
| 19. C22×D4×C131 | C22 | semidirect |
| 22. #121×C131 | C22 | semidirect |
| 23. C2×C4⋊C4×C131 | C22 | semidirect |
| 36. C2×D524 | D4 | semidirect |
| 40. C2×C131⋊C8 | C23 | semidirect |
| 47. C2×D4×C131 | C23 | semidirect |
| 55. C4⋊C4×C131 | C23 | semidirect |
| 68. D524 | C2×D4 | semidirect |
| 76. C23×C131 | D8 | semidirect |
| 100. C22×C131 | C2×D8 | semidirect |
| 114. C2×C131 | #447 | semidirect |
| 119. C131 | C2×#447 | semidirect |
| 123. C2×#121 | D131 | semidirect |
| 134. C22×D4 | C2×D131 | semidirect |
| 140. #121 | C2×D131 | semidirect |
| 141. C2×C4⋊C4 | C2×D131 | semidirect |
| 164. C2×D4 | C22×D131 | semidirect |
| 175. C4⋊C4 | C22×D131 | semidirect |
| 191. C23 | #14523498 | semidirect |
| 225. C22 | C2×#14523498 | semidirect |
| 235. C2 | #22553445 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D524 | 2 |
| C22×#14523498 | 2 |
| #22553445 | 2 |
| C2×#16862166 | 2 |
| C2×C22⋊(C131⋊C8) | 2 |
| C2×#121×C131 | 2 |
| C2×#447 | 131 |