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. #22553940 | C2 | semidirect |
| 3. #22553620 | C2 | semidirect |
| 4. #22553613 | C2 | semidirect |
| 5. #22553608 | C2 | semidirect |
| 6. #22553593 | C2 | semidirect |
| 7. #22553354 | C2 | semidirect |
| 8. C2×#16862180 | C2 | semidirect |
| 11. #424×C131 | C2 | semidirect |
| 42. #14523513 | Q8 | semidirect |
| 123. C131 | #3083 | semidirect |
| 133. #424 | D131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553940 | 2 |
| #22553792 | 2 |
| #22553620 | 2 |
| #22553613 | 2 |
| #22553608 | 2 |
| #22553593 | 2 |
| #22553354 | 2 |
| C2×#16862180 | 2 |
| #22553314 | 2 |
| #22553309 | 2 |
| #424×C131 | 2 |
| #3083 | 131 |