Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
442 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 2. C2×C42×D131 | C2 | semidirect |
| 3. C2×#16862174 | C2 | semidirect |
| 4. C2×#16862172 | C2 | semidirect |
| 5. #22553275 | C2 | semidirect |
| 6. #22553071 | C2 | semidirect |
| 7. #339×C131 | C2 | semidirect |
| 13. #16862226 | C4 | semidirect |
| 14. #16862221 | C4 | semidirect |
| 32. C2×Dic262 | C2×C4 | semidirect |
| 34. C2×D524 | C2×C4 | semidirect |
| 55. C4×Dic131 | D4 | semidirect |
| 61. C4⋊C4×C131 | C2×C4 | semidirect |
| 65. C42×C131 | D4 | semidirect |
| 113. C2×D131 | #104 | semidirect |
| 129. C131 | #1896 | semidirect |
| 137. #339 | D131 | semidirect |
| 186. C4⋊C4 | C4×D131 | semidirect |
| 195. C42 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553824 | 2 |
| C2×C42×D131 | 2 |
| C2×#16862174 | 2 |
| C2×#16862172 | 2 |
| #22553275 | 2 |
| #22553071 | 2 |
| #339×C131 | 2 |
| #1896 | 131 |