Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1408 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1408 conjugacy classes of subgroups — too many to draw. Only its 549 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×#16862293 | C2 | semidirect |
| 2. #22554129 | C2 | direct (N × H) |
| 3. C2×#16862279 | C2 | semidirect |
| 4. C2×#16862268 | C2 | semidirect |
| 5. C22×Dic524 | C2 | semidirect |
| 6. C2×#131×C131 | C2 | semidirect |
| 8. #16862293 | C22 | semidirect |
| 13. #16862279 | C22 | semidirect |
| 14. #16862268 | C22 | semidirect |
| 17. C2×Dic524 | C22 | semidirect |
| 21. #131×C131 | C22 | semidirect |
| 78. C2×C131 | #578 | semidirect |
| 81. C131 | C2×#578 | semidirect |
| 88. C2×#131 | D131 | semidirect |
| 103. #131 | C2×D131 | semidirect |
| 161. C2 | #22554129 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862293 | 2 |
| #22554129 | 2 |
| C2×#16862279 | 2 |
| C2×#16862268 | 2 |
| C22×Dic524 | 2 |
| C2×#131×C131 | 2 |
| C2×#578 | 131 |