Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
1812 conjugacy classes of subgroups; only the 277 normal subgroups are shown.
This group has 1812 conjugacy classes of subgroups — too many to draw. Only its 277 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×D524 | C2 | semidirect |
| 2. C23×C22⋊D131 | C2 | semidirect |
| 3. C22×(C2×D131)⋊C4 | C2 | semidirect |
| 4. #22553221 | C2 | direct (N × H) |
| 5. C2×C131⋊#95 | C2 | semidirect |
| 6. C22×C22⋊C4×C131 | C2 | semidirect |
| 10. C22×D524 | C22 | semidirect |
| 14. C22×C22⋊D131 | C22 | semidirect |
| 17. C2×(C2×D131)⋊C4 | C22 | semidirect |
| 18. C131⋊#95 | C22 | semidirect |
| 23. C2×C22⋊C4×C131 | C22 | semidirect |
| 30. C23×D131 | D4 | semidirect |
| 41. C22×Dic131 | D4 | semidirect |
| 48. C24×C131 | D4 | semidirect |
| 54. C22×C4×C131 | D4 | semidirect |
| 71. C22×D131 | C2×D4 | semidirect |
| 77. C2×Dic131 | C2×D4 | semidirect |
| 91. C23×C131 | C2×D4 | semidirect |
| 99. C2×C4×C131 | C2×D4 | semidirect |
| 128. C2×C131 | #392 | semidirect |
| 135. C131 | C2×#392 | semidirect |
| 140. C22×C22⋊C4 | D131 | semidirect |
| 158. C2×C22⋊C4 | C2×D131 | semidirect |
| 172. C24 | D524 | semidirect |
| 189. C22×C4 | C22⋊D131 | semidirect |
| 221. C23 | C2×D524 | semidirect |
| 235. C2×C4 | C2×C22⋊D131 | semidirect |
| 265. C2 | #22553221 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D524 | 2 |
| C23×C22⋊D131 | 2 |
| C22×(C2×D131)⋊C4 | 2 |
| #22553221 | 2 |
| C2×C131⋊#95 | 2 |
| C22×C22⋊C4×C131 | 2 |
| C2×#392 | 131 |