Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 143 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×#16862277 | C2 | semidirect |
| 3. C2×Q8×Dic131 | C2 | semidirect |
| 4. #22553536 | C2 | semidirect |
| 5. #22553532 | C2 | semidirect |
| 6. #22553520 | C2 | semidirect |
| 7. #22553510 | C2 | semidirect |
| 8. #22553335 | C2 | semidirect |
| 9. #22553314 | C2 | semidirect |
| 10. #22553313 | C2 | semidirect |
| 11. C2×#137×C131 | C2 | semidirect |
| 80. C2×Q8×C131 | D4 | semidirect |
| 150. Dic131 | #137 | semidirect |
| 157. C131 | #3037 | semidirect |
| 160. C2×#137 | D131 | semidirect |
| 210. C2×Q8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862277 | 2 |
| #22553858 | 2 |
| C2×Q8×Dic131 | 2 |
| #22553536 | 2 |
| #22553532 | 2 |
| #22553520 | 2 |
| #22553510 | 2 |
| #22553335 | 2 |
| #22553314 | 2 |
| #22553313 | 2 |
| C2×#137×C131 | 2 |
| #3037 | 131 |