Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
416 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 4. #22553067 | C2 | semidirect |
| 5. #22553066 | C2 | semidirect |
| 6. #22553066 | C2 | semidirect |
| 7. #336×C131 | C2 | semidirect |
| 11. C2×#14523496 | C4 | semidirect |
| 16. C2×C8×D131 | C4 | semidirect |
| 108. C131 | #1729 | semidirect |
| 116. #336 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523496 | 2 |
| C22×C8×D131 | 2 |
| C2×#16862203 | 2 |
| #22553067 | 2 |
| #22553066 | 2 |
| #336×C131 | 2 |
| #1729 | 131 |