Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
412 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 141 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×#16862237 | C2 | semidirect |
| 3. #22553668 | C2 | direct (N × H) |
| 4. C2×#16862170 | C2 | semidirect |
| 7. C2×C8×Dic131 | C2 | semidirect |
| 8. C2×#103×C131 | C2 | semidirect |
| 12. #16862237 | C22 | semidirect |
| 21. #16862170 | C22 | semidirect |
| 24. C8×Dic131 | C22 | semidirect |
| 28. #103×C131 | C22 | semidirect |
| 101. C2×C131 | #488 | semidirect |
| 106. C131 | C2×#488 | semidirect |
| 112. C2×#103 | D131 | semidirect |
| 132. #103 | C2×D131 | semidirect |
| 209. C2 | #22553668 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862237 | 2 |
| C2×#16862235 | 2 |
| #22553668 | 2 |
| C2×#16862170 | 2 |
| C2×#16862168 | 2 |
| C2×#16862166 | 2 |
| C2×C8×Dic131 | 2 |
| C2×#103×C131 | 2 |
| C2×#488 | 131 |