Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
644 conjugacy classes of subgroups; only the 201 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 201 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×#16862244 | C2 | semidirect |
| 4. #22553219 | C2 | semidirect |
| 5. #22553217 | C2 | semidirect |
| 6. #22553207 | C2 | semidirect |
| 7. #22553181 | C2 | semidirect |
| 36. C22×Dic131 | Q8 | semidirect |
| 99. C22×C131 | C4⋊Q8 | semidirect |
| 112. Dic131 | C22⋊Q8 | semidirect |
| 119. C131 | #2857 | semidirect |
| 219. C22 | #16862244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862244 | 2 |
| C2×#16862225 | 2 |
| C22×C4×Dic131 | 2 |
| #22553219 | 2 |
| #22553217 | 2 |
| #22553207 | 2 |
| #22553181 | 2 |
| #22553170 | 2 |
| C2×C22⋊Q8×C131 | 2 |
| #2857 | 131 |