Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
138 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 138 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 |
|---|---|---|
| 2. #22553115 | C2 | semidirect |
| 4. C4×C131⋊C16 | C2 | semidirect |
| 5. #499×C131 | C2 | semidirect |
| 49. C131 | #2242 | semidirect |
| 51. #499 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553696 | 2 |
| #22553115 | 2 |
| #22553112 | 2 |
| C4×C131⋊C16 | 2 |
| #499×C131 | 2 |
| #2242 | 131 |