Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
152 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22553135 | C2 | direct (N × H) |
| 12. M32×C131 | C4 | semidirect |
| 14. C2×C16×C131 | C4 | semidirect |
| 28. C16×C131 | C2×C4 | semidirect |
| 54. C2×C131 | #365 | semidirect |
| 56. C131 | C2×#365 | semidirect |
| 65. M32 | Dic131 | semidirect |
| 67. C2×C16 | Dic131 | semidirect |
| 85. C16 | C2×Dic131 | semidirect |
| 111. C2 | #22553135 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862182 | 2 |
| C2×#16862178 | 2 |
| #22553135 | 2 |
| C2×M32×C131 | 2 |
| C2×#365 | 131 |