Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
166 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 166 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 3. #22553064 | C2 | semidirect |
| 4. Q8⋊(C131⋊C8) | C2 | semidirect |
| 6. #22553034 | C2 | semidirect |
| 7. C8×Q8×C131 | C2 | semidirect |
| 52. Q8×C131 | M16 | semidirect |
| 77. C131 | #1588 | semidirect |
| 79. C8×Q8 | D131 | semidirect |
| 121. Q8 | #14523496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#14523500 | 2 |
| #22553391 | 2 |
| #22553064 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553039 | 2 |
| #22553034 | 2 |
| C8×Q8×C131 | 2 |
| #1588 | 131 |