Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
324 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 97 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×#16862253 | C2 | semidirect |
| 2. C2×#16862173 | C2 | semidirect |
| 3. C2×#16862173 | C2 | semidirect |
| 4. #22553279 | C2 | semidirect |
| 5. #22553077 | C2 | semidirect |
| 6. #22553066 | C2 | semidirect |
| 24. C2×Q16×C131 | C4 | semidirect |
| 25. C2×SD16×C131 | C4 | semidirect |
| 26. C2×SD16×C131 | C4 | semidirect |
| 27. C2×D8×C131 | C4 | semidirect |
| 130. C131 | #1876 | semidirect |
| 143. C2×Q16 | Dic131 | semidirect |
| 144. C2×SD16 | Dic131 | semidirect |
| 145. C2×SD16 | Dic131 | semidirect |
| 146. C2×D8 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862253 | 2 |
| C2×#16862173 | 2 |
| #22553279 | 2 |
| #22553077 | 2 |
| #22553066 | 2 |
| C2×#135×C131 | 2 |
| #1876 | 131 |