Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
224 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 224 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #22553034 | C2 | semidirect |
| 5. C8×C131⋊C8 | C2 | semidirect |
| 6. C8×C131⋊C8 | C2 | semidirect |
| 7. #322×C131 | C2 | semidirect |
| 24. #14523496 | C8 | semidirect |
| 44. C131⋊C8 | C2×C8 | semidirect |
| 45. C131⋊C8 | M16 | semidirect |
| 51. C8×C131 | C2×C8 | semidirect |
| 66. C131 | C8×M16 | semidirect |
| 72. #322 | D131 | semidirect |
| 118. C8 | C8×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553363 | 2 |
| C4×#14523496 | 2 |
| C4×C8×D131 | 2 |
| #22553034 | 2 |
| C8×C131⋊C8 | 2 |
| #322×C131 | 2 |
| C8×M16 | 131 |