Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
262 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 93 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. #22553361 | C2 | semidirect |
| 3. #22553336 | C2 | semidirect |
| 5. #22553084 | C2 | semidirect |
| 6. #22553072 | C2 | semidirect |
| 21. #104×C131 | C4 | semidirect |
| 22. #104×C131 | C4 | semidirect |
| 97. C131 | #1861 | semidirect |
| 119. #104 | Dic131 | semidirect |
| 120. #104 | Dic131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554079 | 2 |
| #22553361 | 2 |
| #22553336 | 2 |
| #22553329 | 2 |
| #22553084 | 2 |
| #22553072 | 2 |
| C2×#104×C131 | 2 |
| #1861 | 131 |