Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
576 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 165 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. C2×Q8×Dic131 | C2 | semidirect |
| 4. #22553234 | C2 | semidirect |
| 5. #22553219 | C2 | semidirect |
| 7. #22553202 | C2 | semidirect |
| 8. C4×Dic131⋊C4 | C2 | semidirect |
| 9. C2×C4⋊Q8×C131 | C2 | semidirect |
| 115. C131 | #2545 | semidirect |
| 117. 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×#16862235 | 2 |
| C2×Q8×Dic131 | 2 |
| #22553234 | 2 |
| #22553219 | 2 |
| #22553214 | 2 |
| #22553202 | 2 |
| C4×Dic131⋊C4 | 2 |
| C2×C4⋊Q8×C131 | 2 |
| #2545 | 131 |