Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
324 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 83 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. C2×#16862254 | C2 | semidirect |
| 3. C2×#16862174 | C2 | semidirect |
| 4. #22553279 | C2 | semidirect |
| 5. #22553076 | C2 | semidirect |
| 6. #22553067 | C2 | semidirect |
| 7. C2×#104×C131 | C2 | semidirect |
| 11. C2×#14523503 | C4 | semidirect |
| 12. C2×#14523501 | C4 | semidirect |
| 13. C2×#14523500 | C4 | semidirect |
| 14. C2×#14523498 | C4 | semidirect |
| 130. C131 | #1876 | semidirect |
| 135. C2×#104 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862266 | 2 |
| C2×#16862254 | 2 |
| C2×#16862174 | 2 |
| #22553279 | 2 |
| #22553076 | 2 |
| #22553067 | 2 |
| C2×#104×C131 | 2 |
| #1876 | 131 |