Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
512 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 229 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. #22553198 | C2 | semidirect |
| 15. C2×C4⋊C4×C131 | C4 | semidirect |
| 66. C131 | #2313 | semidirect |
| 77. C2×C4⋊C4 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553198 | 2 |
| #22553175 | 2 |
| #22553172 | 2 |
| C4×C22⋊Dic131 | 2 |
| C22×C4⋊C4×C131 | 2 |
| #2313 | 131 |