Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
584 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 584 conjugacy classes of subgroups — too many to draw. Only its 157 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. C2×#16862271 | C2 | semidirect |
| 2. C2×#16862243 | C2 | semidirect |
| 3. #22553512 | C2 | semidirect |
| 4. #22553507 | C2 | semidirect |
| 5. #22553336 | C2 | semidirect |
| 6. #22553316 | C2 | semidirect |
| 7. C4×#41×C131 | C2 | semidirect |
| 11. C2×#14523500 | C22 | semidirect |
| 12. C2×#14523498 | C22 | semidirect |
| 17. C4⋊(C131⋊C8) | C22 | semidirect |
| 18. #16862166 | C22 | semidirect |
| 20. C4×Q8×C131 | C22 | semidirect |
| 22. C4×D4×C131 | C22 | semidirect |
| 40. #41×C131 | D4 | semidirect |
| 69. Q8×C131 | C2×D4 | semidirect |
| 72. D4×C131 | C2×D4 | semidirect |
| 96. C4×C131 | AGL(1,ℤ/8) | semidirect |
| 104. C131 | #3038 | semidirect |
| 108. C4×#41 | D131 | semidirect |
| 123. C4×Q8 | C2×D131 | semidirect |
| 125. C4×D4 | C2×D131 | semidirect |
| 134. #41 | D524 | semidirect |
| 168. Q8 | C2×D524 | semidirect |
| 176. D4 | C2×D524 | semidirect |
| 201. C4 | #16862271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862271 | 2 |
| C2×#16862243 | 2 |
| #22553512 | 2 |
| #22553507 | 2 |
| #22553336 | 2 |
| #22553316 | 2 |
| C4×#41×C131 | 2 |
| #3038 | 131 |