Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
142 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 49 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. #22553350 | C2 | semidirect |
| 3. #22553140 | C2 | semidirect |
| 4. #22553138 | C2 | semidirect |
| 5. #22553114 | C2 | semidirect |
| 6. #22553114 | C2 | semidirect |
| 7. C22⋊C16×C131 | C2 | semidirect |
| 69. C131 | #2234 | semidirect |
| 77. C22⋊C16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553548 | 2 |
| #22553350 | 2 |
| #22553140 | 2 |
| #22553138 | 2 |
| #22553114 | 2 |
| C22⋊C16×C131 | 2 |
| #2234 | 131 |