Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
338 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 101 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. C2×#14523503 | C4 | semidirect |
| 75. C2×Dic131 | Q16 | semidirect |
| 119. C131 | #1878 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523503 | 2 |
| C2×#16862211 | 2 |
| C2×#16862171 | 2 |
| #22553219 | 2 |
| #22553074 | 2 |
| #22553066 | 2 |
| C2×#103×C131 | 2 |
| #1878 | 131 |