Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
880 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 2. C2×#16862203 | C2 | semidirect |
| 3. C2×C4⋊C4×D131 | C2 | semidirect |
| 4. #22553219 | C2 | semidirect |
| 5. #22553214 | C2 | semidirect |
| 6. #22553213 | C2 | semidirect |
| 7. #22553190 | C2 | semidirect |
| 8. #22553171 | C2 | semidirect |
| 9. #391×C131 | C2 | semidirect |
| 12. C2×#14523514 | C4 | semidirect |
| 40. C2×D524 | C2×C4 | semidirect |
| 49. C2×C4×D131 | C2×C4 | semidirect |
| 61. C2×Q8×C131 | C2×C4 | semidirect |
| 90. C4×D131 | C22⋊C4 | semidirect |
| 133. C131 | #2311 | semidirect |
| 139. #391 | D131 | semidirect |
| 171. C2×Q8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523514 | 2 |
| C2×#16862203 | 2 |
| C2×C4⋊C4×D131 | 2 |
| #22553219 | 2 |
| #22553214 | 2 |
| #22553213 | 2 |
| #22553190 | 2 |
| #22553171 | 2 |
| #391×C131 | 2 |
| #2311 | 131 |