Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
170 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 51 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×#16862191 | C2 | semidirect |
| 3. #22553696 | C2 | semidirect |
| 4. C4×D1048 | C2 | semidirect |
| 5. #22553117 | C2 | semidirect |
| 6. #22553114 | C2 | semidirect |
| 7. C4⋊C16×C131 | C2 | semidirect |
| 76. C131 | #2210 | semidirect |
| 82. C4⋊C16 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862191 | 2 |
| C2×D2096 | 2 |
| #22553696 | 2 |
| C4×D1048 | 2 |
| #22553117 | 2 |
| #22553114 | 2 |
| C4⋊C16×C131 | 2 |
| #2210 | 131 |