Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
612 conjugacy classes of subgroups; only the 237 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 237 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×Q8×Dic131 | C2 | semidirect |
| 3. #22553219 | C2 | semidirect |
| 5. #22553205 | C2 | semidirect |
| 6. #22553187 | C2 | semidirect |
| 7. #22553182 | C2 | semidirect |
| 8. #22553158 | C2 | semidirect |
| 27. #124×C131 | C4 | semidirect |
| 49. C2×Q8×C131 | C2×C4 | semidirect |
| 56. C22⋊C4×C131 | C2×C4 | semidirect |
| 57. C42×C131 | C2×C4 | semidirect |
| 111. C131 | #2326 | semidirect |
| 125. #124 | Dic131 | semidirect |
| 145. C2×Q8 | C2×Dic131 | semidirect |
| 165. C22⋊C4 | C2×Dic131 | semidirect |
| 169. C42 | C2×Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic131 | 2 |
| C2×D4×Dic131 | 2 |
| #22553219 | 2 |
| #22553215 | 2 |
| #22553205 | 2 |
| #22553187 | 2 |
| #22553182 | 2 |
| #22553158 | 2 |
| C2×#124×C131 | 2 |
| #2326 | 131 |