Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 123 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 |
|---|---|---|
| 77. Dic262 | Q16 | semidirect |
| 112. C131 | #3363 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554042 | 2 |
| #22554037 | 2 |
| #22553661 | 2 |
| #22553605 | 2 |
| #22553604 | 2 |
| #22553521 | 2 |
| #22553519 | 2 |
| C8×Dic262 | 2 |
| C4×Dic524 | 2 |
| #22553404 | 2 |
| #487×C131 | 2 |
| #3363 | 131 |