Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
428 conjugacy classes of subgroups; only the 217 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 217 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 |
|---|---|---|
| 26. #125×C131 | C4 | semidirect |
| 98. C131 | #2336 | semidirect |
| 109. #125 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553211 | 2 |
| #22553198 | 2 |
| #22553180 | 2 |
| C4⋊C4×Dic131 | 2 |
| C4×C4⋊Dic131 | 2 |
| C2×#125×C131 | 2 |
| #2336 | 131 |