Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
704 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 169 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×#16862234 | C2 | semidirect |
| 3. C2×#16862233 | C2 | semidirect |
| 4. #22553228 | C2 | semidirect |
| 5. #22553217 | C2 | semidirect |
| 6. #22553213 | C2 | semidirect |
| 7. #22553191 | C2 | semidirect |
| 8. C4×C4⋊Dic131 | C2 | semidirect |
| 9. C2×C4×D4×C131 | C2 | semidirect |
| 63. C42×C131 | D4 | semidirect |
| 127. C131 | #2544 | semidirect |
| 132. C2×C4×D4 | D131 | semidirect |
| 191. C42 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862242 | 2 |
| C2×#16862234 | 2 |
| C2×#16862233 | 2 |
| #22553228 | 2 |
| #22553217 | 2 |
| #22553213 | 2 |
| #22553191 | 2 |
| C4×C4⋊Dic131 | 2 |
| C2×C4×D4×C131 | 2 |
| #2544 | 131 |