Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
412 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 99 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. C22×#14523496 | C2 | semidirect |
| 3. C2×#16862168 | C2 | semidirect |
| 4. C2×#16862166 | C2 | semidirect |
| 5. #22553169 | C2 | semidirect |
| 6. #22553074 | C2 | semidirect |
| 7. #340×C131 | C2 | semidirect |
| 16. #16862221 | C4 | semidirect |
| 48. C2×C131⋊C8 | D4 | semidirect |
| 58. C2×C8×C131 | D4 | semidirect |
| 145. C131 | #1895 | semidirect |
| 153. #340 | D131 | semidirect |
| 200. C2×C8 | D524 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14523496 | 2 |
| C2×#16862221 | 2 |
| C2×#16862168 | 2 |
| C2×#16862166 | 2 |
| #22553169 | 2 |
| #22553074 | 2 |
| #340×C131 | 2 |
| #1895 | 131 |