Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1840 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1840 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×#16862224 | C2 | direct (N × H) |
| 4. C22×Dic131⋊C4 | C2 | semidirect |
| 5. C22×Dic131⋊C4 | C2 | semidirect |
| 8. C22×C4⋊C4×C131 | C2 | semidirect |
| 11. C22×Dic262 | C22 | semidirect |
| 17. #16862224 | C22 | direct (N × H) |
| 18. C2×Dic131⋊C4 | C22 | semidirect |
| 19. C2×Dic131⋊C4 | C22 | semidirect |
| 25. C2×C4⋊C4×C131 | C22 | semidirect |
| 28. C23×D131 | Q8 | semidirect |
| 31. C2×Dic262 | C23 | semidirect |
| 40. Dic131⋊C4 | C23 | semidirect |
| 41. Dic131⋊C4 | C23 | semidirect |
| 51. C4⋊C4×C131 | C23 | semidirect |
| 55. C22×D131 | C2×Q8 | semidirect |
| 75. C22×C131 | C22⋊Q8 | semidirect |
| 83. C2×D131 | C22×Q8 | semidirect |
| 90. C2×C131 | C2×C22⋊Q8 | semidirect |
| 95. C131 | C22×C22⋊Q8 | semidirect |
| 102. C22×C4⋊C4 | D131 | semidirect |
| 119. C2×C4⋊C4 | C2×D131 | semidirect |
| 145. C4⋊C4 | C22×D131 | semidirect |
| 175. C22 | #16862224 | direct (N × H) |
| 187. C2 | C2×#16862224 | 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×C4×D131 | 2 |
| C2×#16862224 | 2 |
| C22×Dic131⋊C4 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| C22×C4⋊C4×C131 | 2 |
| C22×C22⋊Q8 | 131 |