Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
448 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 1. #22553869 | C2 | semidirect |
| 3. #22553643 | C2 | semidirect |
| 4. #22553603 | C2 | semidirect |
| 5. #22553518 | C2 | semidirect |
| 7. C4×#14523502 | C2 | semidirect |
| 8. #431×C131 | C2 | semidirect |
| 12. #16862246 | C22 | semidirect |
| 13. #16862246 | C22 | semidirect |
| 18. C4×Dic262 | C22 | semidirect |
| 26. #16862178 | C22 | semidirect |
| 27. #16862171 | C22 | semidirect |
| 30. C4⋊C8×C131 | C22 | semidirect |
| 32. C4×C8×C131 | C22 | semidirect |
| 82. C2×C4×C131 | SD16 | semidirect |
| 112. C131 | #3101 | semidirect |
| 121. #431 | D131 | semidirect |
| 141. C4⋊C8 | C2×D131 | semidirect |
| 145. C4×C8 | C2×D131 | semidirect |
| 195. C2×C4 | #14523502 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553869 | 2 |
| C2×C4×D524 | 2 |
| #22553643 | 2 |
| #22553603 | 2 |
| #22553518 | 2 |
| #22553465 | 2 |
| C4×#14523502 | 2 |
| #431×C131 | 2 |
| #3101 | 131 |