Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
386 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×Dic131 | C2 | semidirect |
| 3. #22553648 | C2 | semidirect |
| 5. #22553621 | C2 | semidirect |
| 6. #22553532 | C2 | semidirect |
| 7. #22553468 | C2 | semidirect |
| 8. #22553416 | C2 | semidirect |
| 9. #22553413 | C2 | semidirect |
| 10. #22553366 | C2 | semidirect |
| 131. C131 | #3117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553843 | 2 |
| C2×Q8×Dic131 | 2 |
| #22553648 | 2 |
| #22553628 | 2 |
| #22553621 | 2 |
| #22553532 | 2 |
| #22553468 | 2 |
| #22553416 | 2 |
| #22553413 | 2 |
| #22553366 | 2 |
| #448×C131 | 2 |
| #3117 | 131 |