Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
362 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22553622 | C2 | semidirect |
| 4. #22553618 | C2 | semidirect |
| 5. #22553606 | C2 | semidirect |
| 6. #22553596 | C2 | semidirect |
| 44. C2×Dic262 | Q8 | semidirect |
| 116. C131 | #3082 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553943 | 2 |
| #22553789 | 2 |
| #22553622 | 2 |
| #22553618 | 2 |
| #22553606 | 2 |
| #22553596 | 2 |
| #22553348 | 2 |
| #22553340 | 2 |
| #22553322 | 2 |
| C2×#16862169 | 2 |
| #428×C131 | 2 |
| #3082 | 131 |