Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
314 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 314 conjugacy classes of subgroups — too many to draw. Only its 157 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. #22553442 | C2 | semidirect |
| 3. #22553441 | C2 | semidirect |
| 4. #22553440 | C2 | semidirect |
| 5. #22553439 | C2 | semidirect |
| 91. C131 | #2987 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553865 | 2 |
| #22553442 | 2 |
| #22553441 | 2 |
| #22553440 | 2 |
| #22553439 | 2 |
| #22553373 | 2 |
| #22553370 | 2 |
| #22553366 | 2 |
| #433×C131 | 2 |
| #2987 | 131 |