Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
194 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 194 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 60. Q8×C131 | Q16 | semidirect |
| 83. C131 | #1648 | semidirect |
| 139. Q8 | #14523503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554041 | 2 |
| #22553715 | 2 |
| #22553519 | 2 |
| #22553057 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| #22553042 | 2 |
| #475×C131 | 2 |
| #1648 | 131 |