Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
376 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 376 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. #22553943 | C2 | semidirect |
| 3. #22553617 | C2 | semidirect |
| 4. #22553614 | C2 | semidirect |
| 5. #22553605 | C2 | semidirect |
| 6. #22553590 | C2 | semidirect |
| 7. #22553354 | C2 | semidirect |
| 8. C2×#16862179 | C2 | semidirect |
| 9. #22553340 | C2 | semidirect |
| 64. #41×C131 | Q8 | semidirect |
| 123. C131 | #3083 | semidirect |
| 166. #41 | Dic262 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553943 | 2 |
| #22553795 | 2 |
| #22553617 | 2 |
| #22553614 | 2 |
| #22553605 | 2 |
| #22553590 | 2 |
| #22553354 | 2 |
| C2×#16862179 | 2 |
| #22553340 | 2 |
| #22553308 | 2 |
| #417×C131 | 2 |
| #3083 | 131 |