Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
420 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 189 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. #16862205 | C4 | semidirect |
| 12. C2×C4⋊C4×C131 | C4 | semidirect |
| 14. C2×C42×C131 | C4 | semidirect |
| 75. C131 | #1740 | semidirect |
| 86. C2×C4⋊C4 | Dic131 | semidirect |
| 90. C2×C42 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862205 | 2 |
| #22553079 | 2 |
| C2×#117×C131 | 2 |
| #1740 | 131 |