Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
672 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C2×#16862225 | C2 | semidirect |
| 3. #22553239 | C2 | semidirect |
| 4. #22553225 | C2 | semidirect |
| 5. #22553203 | C2 | semidirect |
| 6. #22553173 | C2 | semidirect |
| 8. C4×C22⋊C4×C131 | C2 | semidirect |
| 10. C22×Dic262 | C22 | semidirect |
| 13. C2×C4⋊Dic131 | C22 | semidirect |
| 14. C2×Dic131⋊C4 | C22 | semidirect |
| 21. C131⋊#95 | C22 | semidirect |
| 22. C131⋊#95 | C22 | semidirect |
| 25. C2×C42×C131 | C22 | semidirect |
| 26. #95×C131 | C22 | semidirect |
| 110. C131 | #2561 | semidirect |
| 119. C4×C22⋊C4 | D131 | semidirect |
| 134. C2×C42 | C2×D131 | semidirect |
| 137. #95 | C2×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862225 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| #22553239 | 2 |
| #22553225 | 2 |
| #22553203 | 2 |
| #22553173 | 2 |
| #22553167 | 2 |
| C4×C22⋊C4×C131 | 2 |
| #2561 | 131 |