Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
420 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×D524 | C2 | semidirect |
| 3. #22553664 | C2 | semidirect |
| 4. #22553644 | C2 | semidirect |
| 5. #22553542 | C2 | semidirect |
| 6. #22553518 | C2 | semidirect |
| 7. #22553452 | C2 | semidirect |
| 8. C4×#14523500 | C2 | semidirect |
| 9. #22553377 | C2 | semidirect |
| 10. #103×D131 | C2 | semidirect |
| 11. #475×C131 | C2 | semidirect |
| 85. D524 | SD16 | semidirect |
| 98. Q8×C131 | #41 | semidirect |
| 128. C131 | #3298 | semidirect |
| 134. #475 | D131 | semidirect |
| 213. Q8 | #14523514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D524 | 2 |
| #22553965 | 2 |
| #22553664 | 2 |
| #22553644 | 2 |
| #22553542 | 2 |
| #22553518 | 2 |
| #22553452 | 2 |
| C4×#14523500 | 2 |
| #22553377 | 2 |
| #103×D131 | 2 |
| #475×C131 | 2 |
| #3298 | 131 |