Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
332 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 145 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 |
|---|---|---|
| 12. C4⋊Q8×C131 | C4 | semidirect |
| 53. C4×C131 | #103 | semidirect |
| 62. C131 | #1956 | semidirect |
| 71. C4⋊Q8 | Dic131 | semidirect |
| 117. C4 | #16862170 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862170 | 2 |
| C2×C4×C131⋊C8 | 2 |
| #22553182 | 2 |
| C2×C4⋊Q8×C131 | 2 |
| #1956 | 131 |