Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
460 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 127 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. C2×Q16×D131 | C2 | semidirect |
| 4. #22553571 | C2 | semidirect |
| 5. #22553570 | C2 | semidirect |
| 6. #22553567 | C2 | semidirect |
| 7. #22553552 | C2 | semidirect |
| 8. #22553551 | C2 | semidirect |
| 9. #22553347 | C2 | semidirect |
| 10. #22553319 | C2 | semidirect |
| 11. #470×C131 | C2 | semidirect |
| 133. C131 | #3059 | semidirect |
| 141. #470 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D131 | 2 |
| C2×#16862254 | 2 |
| #22553885 | 2 |
| #22553571 | 2 |
| #22553570 | 2 |
| #22553567 | 2 |
| #22553552 | 2 |
| #22553551 | 2 |
| #22553347 | 2 |
| #22553319 | 2 |
| #470×C131 | 2 |
| #3059 | 131 |