Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
130 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 130 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 |
|---|---|---|
| 21. Q16×C131 | Q8 | semidirect |
| 51. C131 | #2227 | semidirect |
| 70. Q16 | Dic262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553717 | 2 |
| #22553137 | 2 |
| C4⋊(C131⋊C16) | 2 |
| #22553116 | 2 |
| C4×Q16×C131 | 2 |
| #2227 | 131 |