Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
480 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 480 conjugacy classes of subgroups — too many to draw. Only its 173 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×#16862246 | C2 | semidirect |
| 3. #22553603 | C2 | direct (N × H) |
| 4. C2×#16862178 | C2 | semidirect |
| 6. C2×C4⋊C8×C131 | C2 | semidirect |
| 11. #16862246 | C22 | semidirect |
| 18. #16862178 | C22 | semidirect |
| 22. C4⋊C8×C131 | C22 | semidirect |
| 28. C2×D524 | Q8 | semidirect |
| 54. D524 | C2×Q8 | semidirect |
| 85. C2×C131 | #476 | semidirect |
| 90. C131 | C2×#476 | semidirect |
| 96. C2×C4⋊C8 | D131 | semidirect |
| 112. C4⋊C8 | C2×D131 | semidirect |
| 177. C2 | #22553603 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862246 | 2 |
| C2×C4×D524 | 2 |
| #22553603 | 2 |
| C2×#16862178 | 2 |
| C2×#16862168 | 2 |
| C2×C4⋊C8×C131 | 2 |
| C2×#476 | 131 |