Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
228 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 73 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 |
|---|---|---|
| 5. #16862246 | C4 | semidirect |
| 6. #16862246 | C4 | semidirect |
| 11. C4×Dic262 | C4 | semidirect |
| 75. C131 | #1506 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553869 | 2 |
| #22553158 | 2 |
| #22553050 | 2 |
| #432×C131 | 2 |
| #1506 | 131 |