Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16862238 | C2 | semidirect |
| 2. #22553619 | C2 | semidirect |
| 3. #22553612 | C2 | semidirect |
| 4. #22553355 | C2 | semidirect |
| 5. #22553336 | C2 | semidirect |
| 90. C131 | #3080 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862238 | 2 |
| #22553619 | 2 |
| #22553612 | 2 |
| #22553355 | 2 |
| #22553336 | 2 |
| #22553313 | 2 |
| C4×#41×C131 | 2 |
| #3080 | 131 |