Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
388 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 388 conjugacy classes of subgroups — too many to draw. Only its 139 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. #22553663 | C2 | semidirect |
| 4. #22553648 | C2 | semidirect |
| 5. #22553608 | C2 | semidirect |
| 6. #22553553 | C2 | semidirect |
| 7. #22553523 | C2 | semidirect |
| 8. #22553470 | C2 | semidirect |
| 9. C4×Dic524 | C2 | semidirect |
| 10. C2×#16862171 | C2 | semidirect |
| 93. D4×C131 | Q16 | semidirect |
| 122. C131 | #3299 | semidirect |
| 208. D4 | Dic524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22554019 | 2 |
| D4×Dic262 | 2 |
| #22553663 | 2 |
| #22553648 | 2 |
| #22553608 | 2 |
| #22553553 | 2 |
| #22553523 | 2 |
| #22553470 | 2 |
| C4×Dic524 | 2 |
| C2×#16862171 | 2 |
| C8×D4×C131 | 2 |
| #3299 | 131 |