Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
230 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 13. #16862177 | C4 | semidirect |
| 96. C131 | #1920 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862177 | 2 |
| #22553210 | 2 |
| #22553074 | 2 |
| #22553067 | 2 |
| C4×C4⋊C4×C131 | 2 |
| #1920 | 131 |