Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
472 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 472 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×#16862279 | C2 | semidirect |
| 3. #22553883 | C2 | semidirect |
| 4. #22553570 | C2 | semidirect |
| 5. #22553558 | C2 | semidirect |
| 6. #22553553 | C2 | semidirect |
| 7. #22553541 | C2 | semidirect |
| 8. #22553354 | C2 | semidirect |
| 9. #22553309 | C2 | semidirect |
| 10. C2×#16862171 | C2 | semidirect |
| 11. C2×#131×C131 | C2 | semidirect |
| 79. M16×C131 | D4 | semidirect |
| 143. C131 | #3063 | semidirect |
| 146. C2×#131 | D131 | semidirect |
| 210. M16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862279 | 2 |
| #22553890 | 2 |
| #22553883 | 2 |
| #22553570 | 2 |
| #22553558 | 2 |
| #22553553 | 2 |
| #22553541 | 2 |
| #22553354 | 2 |
| #22553309 | 2 |
| C2×#16862171 | 2 |
| C2×#131×C131 | 2 |
| #3063 | 131 |