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×#16862173 | C2 | semidirect |
| 4. #22553275 | C2 | semidirect |
| 5. #22553073 | C2 | semidirect |
| 6. #22553072 | C2 | semidirect |
| 7. C2×#104×C131 | C2 | semidirect |
| 12. #16862222 | C4 | semidirect |
| 13. #16862217 | C4 | semidirect |
| 42. C4⋊Dic131 | C2×C4 | semidirect |
| 50. C4×Dic131 | D4 | semidirect |
| 55. C2×Q8×C131 | C2×C4 | semidirect |
| 57. C2×D4×C131 | C2×C4 | semidirect |
| 65. C42×C131 | D4 | semidirect |
| 113. C2×D131 | #104 | semidirect |
| 129. C131 | #1896 | semidirect |
| 134. C2×#104 | D131 | semidirect |
| 162. C2×Q8 | C4×D131 | semidirect |
| 165. C2×D4 | C4×D131 | semidirect |
| 195. C42 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553819 | 2 |
| C2×C42×D131 | 2 |
| C2×#16862173 | 2 |
| #22553275 | 2 |
| #22553073 | 2 |
| #22553072 | 2 |
| C2×#104×C131 | 2 |
| #1896 | 131 |