Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1036 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 1036 conjugacy classes of subgroups — too many to draw. Only its 253 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. C23×Dic262 | C2 | semidirect |
| 4. #22553225 | C2 | direct (N × H) |
| 5. C2×C131⋊#95 | C2 | semidirect |
| 6. C2×#95×C131 | C2 | semidirect |
| 10. C22×Dic262 | C22 | semidirect |
| 17. C131⋊#95 | C22 | semidirect |
| 20. #95×C131 | C22 | semidirect |
| 25. C23×D131 | Q8 | semidirect |
| 56. C22×D131 | C2×Q8 | semidirect |
| 98. C2×C131 | #393 | semidirect |
| 105. C131 | C2×#393 | semidirect |
| 112. C2×#95 | D131 | semidirect |
| 126. #95 | C2×D131 | semidirect |
| 205. C2 | #22553225 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×Dic262 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| #22553225 | 2 |
| C2×C131⋊#95 | 2 |
| C2×#95×C131 | 2 |
| C2×#393 | 131 |