Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
428 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 125 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. C2×#16862211 | C2 | semidirect |
| 3. #22553630 | C2 | semidirect |
| 4. #22553596 | C2 | semidirect |
| 5. #22553511 | C2 | semidirect |
| 6. #22553453 | C2 | semidirect |
| 7. #22553450 | C2 | semidirect |
| 8. #22553403 | C2 | semidirect |
| 9. #22553399 | C2 | semidirect |
| 10. #22553362 | C2 | semidirect |
| 11. #481×C131 | C2 | semidirect |
| 86. Dic262 | #41 | semidirect |
| 96. C2×Dic131 | SD16 | semidirect |
| 140. C131 | #3103 | semidirect |
| 145. #481 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553857 | 2 |
| C2×#16862211 | 2 |
| #22553630 | 2 |
| #22553596 | 2 |
| #22553511 | 2 |
| #22553453 | 2 |
| #22553450 | 2 |
| #22553403 | 2 |
| #22553399 | 2 |
| #22553362 | 2 |
| #481×C131 | 2 |
| #3103 | 131 |