Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
228 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 101. C131 | #1917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic131⋊C8 | 2 |
| C2×#16862156 | 2 |
| C4×C4⋊Dic131 | 2 |
| #22553067 | 2 |
| #22553066 | 2 |
| #336×C131 | 2 |
| #1917 | 131 |