Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
240 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 240 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 |
|---|---|---|
| 11. C4⋊Q8×C131 | C4 | semidirect |
| 12. C4⋊Q8×C131 | C4 | semidirect |
| 17. C4×Q8×C131 | C4 | semidirect |
| 79. C131 | #1503 | semidirect |
| 85. C4⋊Q8 | Dic131 | semidirect |
| 86. C4⋊Q8 | Dic131 | semidirect |
| 91. C4×Q8 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553365 | 2 |
| C4×C4⋊Dic131 | 2 |
| #22553049 | 2 |
| #533×C131 | 2 |
| #1503 | 131 |