Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 402 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 |
|---|---|---|
| 3. C2×#16862169 | C2 | semidirect |
| 5. #22553217 | C2 | semidirect |
| 6. #22553066 | C2 | semidirect |
| 7. #340×C131 | C2 | semidirect |
| 13. C2×#14523502 | C4 | semidirect |
| 32. C2×Dic262 | C2×C4 | semidirect |
| 57. C2×C8×C131 | C2×C4 | semidirect |
| 85. C2×Dic131 | SD16 | semidirect |
| 133. C131 | #1877 | semidirect |
| 140. #340 | D131 | semidirect |
| 188. C2×C8 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| C2×#16862208 | 2 |
| C2×#16862169 | 2 |
| C2×#16862166 | 2 |
| #22553217 | 2 |
| #22553066 | 2 |
| #340×C131 | 2 |
| #1877 | 131 |