Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
564 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 181 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×#16862246 | C2 | semidirect |
| 2. #22553224 | C2 | semidirect |
| 4. #22553177 | C2 | semidirect |
| 5. #22553172 | C2 | semidirect |
| 6. C4×C4⋊Dic131 | C2 | semidirect |
| 35. C2×D4×C131 | Q8 | semidirect |
| 90. C131 | #2563 | semidirect |
| 119. C2×D4 | Dic262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862246 | 2 |
| #22553224 | 2 |
| #22553215 | 2 |
| #22553177 | 2 |
| #22553172 | 2 |
| C4×C4⋊Dic131 | 2 |
| C2×C4×D4×C131 | 2 |
| #2563 | 131 |