Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #22554125 | C2 | semidirect |
| 2. #22553754 | C2 | semidirect |
| 3. #22553753 | C2 | semidirect |
| 4. #22553745 | C2 | semidirect |
| 5. #22553744 | C2 | semidirect |
| 6. Q32×D131 | C2 | semidirect |
| 7. #22553728 | C2 | semidirect |
| 8. C2×Q32×C131 | C2 | semidirect |
| 81. C131 | #3417 | semidirect |
| 89. C2×Q32 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554125 | 2 |
| #22553754 | 2 |
| #22553753 | 2 |
| #22553745 | 2 |
| #22553744 | 2 |
| Q32×D131 | 2 |
| #22553728 | 2 |
| C2×Q32×C131 | 2 |
| #3417 | 131 |