Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
200 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 200 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 59. Q8×C131 | Q16 | semidirect |
| 83. C131 | #1645 | semidirect |
| 139. Q8 | #14523503 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553662 | 2 |
| #22553597 | 2 |
| #22553522 | 2 |
| #22553061 | 2 |
| Q8⋊(C131⋊C8) | 2 |
| Q82×C131 | 2 |
| #1645 | 131 |