Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
402 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 107 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×#16862171 | C2 | semidirect |
| 4. #22553217 | C2 | semidirect |
| 5. #22553074 | C2 | semidirect |
| 6. #22553066 | C2 | semidirect |
| 12. C2×#14523501 | C4 | semidirect |
| 31. C2×Dic262 | C2×C4 | semidirect |
| 42. C2×C131⋊C8 | C2×C4 | semidirect |
| 78. C2×Dic131 | SD16 | semidirect |
| 133. C131 | #1877 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523501 | 2 |
| C2×D4×Dic131 | 2 |
| C2×#16862171 | 2 |
| #22553217 | 2 |
| #22553074 | 2 |
| #22553066 | 2 |
| C2×#102×C131 | 2 |
| #1877 | 131 |