Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
358 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 358 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 4. #22553620 | C2 | semidirect |
| 5. #22553523 | C2 | semidirect |
| 7. #22553420 | C2 | semidirect |
| 8. C4×Dic524 | C2 | semidirect |
| 95. C131 | #3127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553924 | 2 |
| #22553789 | 2 |
| #22553654 | 2 |
| #22553620 | 2 |
| #22553523 | 2 |
| #22553470 | 2 |
| #22553420 | 2 |
| C4×Dic524 | 2 |
| #433×C131 | 2 |
| #3127 | 131 |