Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
568 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 161 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. #22553251 | C2 | semidirect |
| 3. #22553238 | C2 | semidirect |
| 5. #22553223 | C2 | semidirect |
| 6. C4×(C2×D131)⋊C4 | C2 | semidirect |
| 7. #22553158 | C2 | semidirect |
| 8. C2×C4×Q8×C131 | C2 | semidirect |
| 96. C131 | #2398 | semidirect |
| 98. C2×C4×Q8 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D524 | 2 |
| #22553251 | 2 |
| #22553238 | 2 |
| #22553229 | 2 |
| #22553223 | 2 |
| C4×(C2×D131)⋊C4 | 2 |
| #22553158 | 2 |
| C2×C4×Q8×C131 | 2 |
| #2398 | 131 |