Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
480 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862246 | C2 | semidirect |
| 4. #22553523 | C2 | semidirect |
| 5. #22553518 | C2 | semidirect |
| 6. #22553322 | C2 | semidirect |
| 7. #423×C131 | C2 | semidirect |
| 87. C4×C131 | #137 | semidirect |
| 97. C131 | #3039 | semidirect |
| 104. #423 | D131 | semidirect |
| 188. C4 | #16862279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| C2×#16862246 | 2 |
| C4×#14523513 | 2 |
| #22553523 | 2 |
| #22553518 | 2 |
| #22553322 | 2 |
| #423×C131 | 2 |
| #3039 | 131 |