Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22553620 | C2 | direct (N × H) |
| 91. C2×C131 | #479 | semidirect |
| 95. C131 | C2×#479 | semidirect |
| 187. C2 | #22553620 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862238 | 2 |
| C2×C4×Dic262 | 2 |
| #22553620 | 2 |
| C2×#16862180 | 2 |
| C2×#16862178 | 2 |
| C2×#16862171 | 2 |
| C2×C4⋊C8×C131 | 2 |
| C2×#479 | 131 |