Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
120 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 53 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 |
|---|---|---|
| 27. C131⋊C16 | Q8 | semidirect |
| 31. C16×C131 | Q8 | semidirect |
| 55. C131 | #2255 | semidirect |
| 87. C16 | Dic262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553716 | 2 |
| #22553713 | 2 |
| #22553140 | 2 |
| #22553139 | 2 |
| #22553137 | 2 |
| #22553087 | 2 |
| #366×C131 | 2 |
| #2255 | 131 |