Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 384 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 |
|---|---|---|
| 1. C2×#16862237 | C2 | semidirect |
| 3. #22553622 | C2 | semidirect |
| 4. #22553618 | C2 | semidirect |
| 5. #22553615 | C2 | semidirect |
| 6. #22553611 | C2 | semidirect |
| 7. #22553355 | C2 | semidirect |
| 8. #22553335 | C2 | semidirect |
| 11. #428×C131 | C2 | semidirect |
| 135. C131 | #3080 | semidirect |
| 144. #428 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862237 | 2 |
| #22553780 | 2 |
| #22553622 | 2 |
| #22553618 | 2 |
| #22553615 | 2 |
| #22553611 | 2 |
| #22553355 | 2 |
| #22553335 | 2 |
| #22553314 | 2 |
| #22553311 | 2 |
| #428×C131 | 2 |
| #3080 | 131 |