Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
228 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 79 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 |
|---|---|---|
| 2. C2×#16862185 | C2 | semidirect |
| 3. C2×C16×D131 | C2 | semidirect |
| 4. C22⋊(C131⋊C16) | C2 | semidirect |
| 5. (C2×D131)⋊C16 | C2 | semidirect |
| 6. (C2×D131)⋊C16 | C2 | semidirect |
| 7. C22⋊C16×C131 | C2 | semidirect |
| 92. C131 | #2113 | semidirect |
| 100. C22⋊C16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862252 | 2 |
| C2×#16862185 | 2 |
| C2×C16×D131 | 2 |
| C22⋊(C131⋊C16) | 2 |
| (C2×D131)⋊C16 | 2 |
| C22⋊C16×C131 | 2 |
| #2113 | 131 |