Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
196 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 1. C2×#16862191 | C2 | semidirect |
| 2. C2×#16862190 | C2 | semidirect |
| 3. C2×#16862189 | C2 | semidirect |
| 4. #22553690 | C2 | semidirect |
| 6. C16×Dic131 | C2 | semidirect |
| 7. C2×SD32×C131 | C2 | semidirect |
| 35. C131⋊C16 | D4 | semidirect |
| 43. C16×C131 | D4 | semidirect |
| 71. Dic131 | SD32 | semidirect |
| 76. C131 | #2248 | semidirect |
| 81. C2×SD32 | D131 | semidirect |
| 120. C16 | C22⋊D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862191 | 2 |
| C2×#16862190 | 2 |
| C2×#16862189 | 2 |
| #22553690 | 2 |
| #22553687 | 2 |
| C16×Dic131 | 2 |
| C2×SD32×C131 | 2 |
| #2248 | 131 |