Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
484 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862268 | C2 | semidirect |
| 2. #22553890 | C2 | semidirect |
| 3. #22553558 | C2 | semidirect |
| 4. #22553553 | C2 | semidirect |
| 5. #22553548 | C2 | semidirect |
| 6. C2×#16862180 | C2 | semidirect |
| 7. #22553314 | C2 | semidirect |
| 8. C2×#131×C131 | C2 | semidirect |
| 56. C2×C8×C131 | D4 | semidirect |
| 108. C131 | #3061 | semidirect |
| 111. C2×#131 | D131 | semidirect |
| 160. C2×C8 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862268 | 2 |
| #22553890 | 2 |
| #22553558 | 2 |
| #22553553 | 2 |
| #22553548 | 2 |
| C2×#16862180 | 2 |
| #22553314 | 2 |
| C2×#131×C131 | 2 |
| #3061 | 131 |