Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
676 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 676 conjugacy classes of subgroups — too many to draw. Only its 181 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×#16862235 | C2 | semidirect |
| 3. #22553229 | C2 | semidirect |
| 4. #22553214 | C2 | semidirect |
| 5. #22553213 | C2 | semidirect |
| 6. C4×C4⋊Dic131 | C2 | semidirect |
| 7. C2×C4×Q8×C131 | C2 | semidirect |
| 39. C2×Q8×C131 | D4 | semidirect |
| 88. C4×C131 | #124 | semidirect |
| 96. C131 | #2548 | semidirect |
| 100. C2×C4×Q8 | D131 | semidirect |
| 124. C2×Q8 | D524 | semidirect |
| 186. C4 | #16862235 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862243 | 2 |
| C2×#16862235 | 2 |
| #22553229 | 2 |
| #22553214 | 2 |
| #22553213 | 2 |
| C4×C4⋊Dic131 | 2 |
| C2×C4×Q8×C131 | 2 |
| #2548 | 131 |