Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
402 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 103 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×#16862171 | C2 | semidirect |
| 5. #22553218 | C2 | semidirect |
| 6. #22553075 | C2 | semidirect |
| 7. #336×C131 | C2 | semidirect |
| 13. C2×#14523502 | C4 | semidirect |
| 32. C2×Dic262 | C2×C4 | semidirect |
| 59. C2×C8×C131 | C2×C4 | semidirect |
| 93. C2×C4×C131 | SD16 | semidirect |
| 133. C131 | #1877 | semidirect |
| 141. #336 | D131 | semidirect |
| 188. C2×C8 | C4×D131 | semidirect |
| 227. C2×C4 | #14523502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523502 | 2 |
| C2×C4×D524 | 2 |
| C2×#16862171 | 2 |
| C2×#16862168 | 2 |
| #22553218 | 2 |
| #22553075 | 2 |
| #336×C131 | 2 |
| #1877 | 131 |