Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
456 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 456 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. #22553211 | C2 | semidirect |
| 3. #22553198 | C2 | semidirect |
| 5. #22553182 | C2 | semidirect |
| 6. #22553180 | C2 | semidirect |
| 18. #126×C131 | C4 | semidirect |
| 35. C4⋊C4×C131 | C2×C4 | semidirect |
| 37. C42×C131 | C2×C4 | semidirect |
| 72. C131 | #2383 | semidirect |
| 82. #126 | Dic131 | semidirect |
| 106. C4⋊C4 | C2×Dic131 | semidirect |
| 110. C42 | C2×Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553211 | 2 |
| #22553205 | 2 |
| #22553198 | 2 |
| #22553187 | 2 |
| #22553182 | 2 |
| #22553180 | 2 |
| C2×#126×C131 | 2 |
| #2383 | 131 |