Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
172 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 172 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 |
|---|---|---|
| 1. #22553715 | C2 | semidirect |
| 4. #22553064 | C2 | semidirect |
| 5. #22553059 | C2 | semidirect |
| 6. #22553058 | C2 | semidirect |
| 48. C131⋊C8 | SD16 | semidirect |
| 78. C131 | #1673 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553715 | 2 |
| #22553517 | 2 |
| D4×C131⋊C8 | 2 |
| #22553064 | 2 |
| #22553059 | 2 |
| #22553058 | 2 |
| #461×C131 | 2 |
| #1673 | 131 |