Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1880 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 645 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 |
| 3. C2×#16862234 | C2 | direct (N × H) |
| 4. C22×(C2×D131)⋊C4 | C2 | semidirect |
| 5. C22×C42×C131 | C2 | semidirect |
| 8. C22×Dic262 | C22 | semidirect |
| 12. #16862234 | C22 | direct (N × H) |
| 13. C2×(C2×D131)⋊C4 | C22 | semidirect |
| 16. C2×C42×C131 | C22 | semidirect |
| 21. C2×Dic262 | C23 | semidirect |
| 26. (C2×D131)⋊C4 | C23 | semidirect |
| 32. C42×C131 | C23 | semidirect |
| 48. C22×C131 | #124 | semidirect |
| 58. C2×C131 | C2×#124 | semidirect |
| 62. C131 | C22×#124 | semidirect |
| 68. C22×C42 | D131 | semidirect |
| 79. C2×C42 | C2×D131 | semidirect |
| 95. C42 | C22×D131 | semidirect |
| 114. C22 | #16862234 | direct (N × H) |
| 122. C2 | C2×#16862234 | 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 |
| C23×D524 | 2 |
| C2×#16862234 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| C22×C42×C131 | 2 |
| C22×#124 | 131 |