Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
298 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 23. #103×C131 | C4 | semidirect |
| 71. Q8×C131 | C4⋊C4 | semidirect |
| 109. C131 | #1865 | semidirect |
| 132. #103 | Dic131 | semidirect |
| 168. Q8 | C4⋊Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×Dic131 | 2 |
| C2×#16862178 | 2 |
| C2×#16862170 | 2 |
| #22553211 | 2 |
| #22553074 | 2 |
| #22553066 | 2 |
| C2×#103×C131 | 2 |
| #1865 | 131 |