Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
438 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16862208 | C2 | semidirect |
| 3. C2×#16862168 | C2 | semidirect |
| 4. #22553215 | C2 | semidirect |
| 5. #22553074 | C2 | semidirect |
| 6. #22553066 | C2 | semidirect |
| 7. C2×#102×C131 | C2 | semidirect |
| 12. C2×#14523498 | C4 | semidirect |
| 42. C2×C131⋊C8 | C2×C4 | semidirect |
| 56. C2×D4×C131 | C2×C4 | semidirect |
| 74. D524 | C22⋊C4 | semidirect |
| 83. C2×Dic131 | D8 | semidirect |
| 146. C131 | #1879 | semidirect |
| 151. C2×#102 | D131 | semidirect |
| 186. C2×D4 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523498 | 2 |
| C2×#16862208 | 2 |
| C2×#16862168 | 2 |
| #22553215 | 2 |
| #22553074 | 2 |
| #22553066 | 2 |
| C2×#102×C131 | 2 |
| #1879 | 131 |