Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
360 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 360 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 |
|---|---|---|
| 3. #22553322 | C2 | semidirect |
| 4. #22553320 | C2 | semidirect |
| 6. #22553072 | C2 | semidirect |
| 7. #339×C131 | C2 | semidirect |
| 12. #16862234 | C4 | semidirect |
| 30. C2×Dic262 | C2×C4 | semidirect |
| 56. C42×C131 | C2×C4 | semidirect |
| 107. C131 | #1885 | semidirect |
| 115. #339 | D131 | semidirect |
| 164. C42 | C4×D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16862234 | 2 |
| #22553786 | 2 |
| #22553322 | 2 |
| #22553320 | 2 |
| C2×#16862162 | 2 |
| #22553072 | 2 |
| #339×C131 | 2 |
| #1885 | 131 |