Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
336 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 117 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 |
|---|---|---|
| 1. #22554041 | C2 | semidirect |
| 4. #22553662 | C2 | semidirect |
| 5. #22553621 | C2 | semidirect |
| 8. #22553436 | C2 | semidirect |
| 9. Q16×Dic131 | C2 | semidirect |
| 11. #462×C131 | C2 | semidirect |
| 115. C131 | #3364 | semidirect |
| 124. #462 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554041 | 2 |
| #22554036 | 2 |
| #22553668 | 2 |
| #22553662 | 2 |
| #22553621 | 2 |
| #22553593 | 2 |
| #22553536 | 2 |
| #22553436 | 2 |
| Q16×Dic131 | 2 |
| C4×#14523500 | 2 |
| #462×C131 | 2 |
| #3364 | 131 |