Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
178 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 178 conjugacy classes of subgroups — too many to draw. Only its 61 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. C2×Dic1048 | C2 | semidirect |
| 4. #22553692 | C2 | semidirect |
| 5. #346×C131 | C2 | semidirect |
| 56. C131 | #2251 | semidirect |
| 62. #346 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic1048 | 2 |
| C2×#16862191 | 2 |
| #22553696 | 2 |
| #22553692 | 2 |
| #346×C131 | 2 |
| #2251 | 131 |