Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
372 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×D524 | C2 | semidirect |
| 2. #22553671 | C2 | semidirect |
| 3. #22553662 | C2 | semidirect |
| 4. #22553607 | C2 | semidirect |
| 5. #22553592 | C2 | semidirect |
| 7. #22553514 | C2 | semidirect |
| 8. #22553443 | C2 | semidirect |
| 9. #22553410 | C2 | semidirect |
| 11. #556×C131 | C2 | semidirect |
| 122. C131 | #3367 | semidirect |
| 124. #556 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×D524 | 2 |
| #22553671 | 2 |
| #22553662 | 2 |
| #22553607 | 2 |
| #22553592 | 2 |
| #22553524 | 2 |
| #22553514 | 2 |
| #22553443 | 2 |
| #22553410 | 2 |
| C4×#14523498 | 2 |
| #556×C131 | 2 |
| #3367 | 131 |