Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
384 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 141 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. #22553608 | C2 | semidirect |
| 5. #22553523 | C2 | semidirect |
| 7. C4×Dic524 | C2 | semidirect |
| 77. C2×C4×C131 | Q16 | semidirect |
| 103. C131 | #3104 | semidirect |
| 181. C2×C4 | Dic524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553869 | 2 |
| C2×C4×Dic262 | 2 |
| #22553648 | 2 |
| #22553608 | 2 |
| #22553523 | 2 |
| #22553470 | 2 |
| C4×Dic524 | 2 |
| #431×C131 | 2 |
| #3104 | 131 |