Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
294 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 294 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 3. #22553049 | C2 | semidirect |
| 11. C22×Q8×C131 | C4 | semidirect |
| 15. C22⋊Q8×C131 | C4 | semidirect |
| 18. C2×C4⋊C4×C131 | C4 | semidirect |
| 94. C131 | #1508 | semidirect |
| 100. C22×Q8 | Dic131 | semidirect |
| 105. C22⋊Q8 | Dic131 | semidirect |
| 108. C2×C4⋊C4 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553276 | 2 |
| C4×C22⋊Dic131 | 2 |
| #22553049 | 2 |
| C2×C22⋊Q8×C131 | 2 |
| #1508 | 131 |