Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
292 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 95 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×C8×Dic131 | C2 | semidirect |
| 4. #22553208 | C2 | semidirect |
| 5. #22553075 | C2 | semidirect |
| 6. #22553074 | C2 | semidirect |
| 15. #16862167 | C4 | semidirect |
| 118. C131 | #1934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862167 | 2 |
| C2×C8×Dic131 | 2 |
| #22553215 | 2 |
| #22553208 | 2 |
| #22553075 | 2 |
| #22553074 | 2 |
| C2×#102×C131 | 2 |
| #1934 | 131 |