Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
688 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 688 conjugacy classes of subgroups — too many to draw. Only its 213 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. #22553215 | C2 | semidirect |
| 2. #22553205 | C2 | semidirect |
| 3. #22553192 | C2 | semidirect |
| 4. #22553168 | C2 | semidirect |
| 6. C23×Dic131 | C22 | semidirect |
| 7. C2×C4⋊Dic131 | C22 | semidirect |
| 10. C2×C22⋊Dic131 | C22 | semidirect |
| 11. C2×C4×Dic131 | C22 | semidirect |
| 12. C131⋊#95 | C22 | semidirect |
| 15. #120×C131 | C4 | semidirect |
| 27. C24×C131 | C2×C4 | semidirect |
| 34. C22⋊C4×C131 | C2×C4 | semidirect |
| 76. C131 | #2375 | semidirect |
| 86. #120 | Dic131 | semidirect |
| 96. C24 | C2×Dic131 | semidirect |
| 110. C22⋊C4 | C2×Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553215 | 2 |
| #22553205 | 2 |
| #22553192 | 2 |
| #22553168 | 2 |
| C2×#120×C131 | 2 |
| #2375 | 131 |