Finite Group DatabasebetaFinite Group DatabasebetaOrder 16768.
396 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 125 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. #22553984 | C2 | semidirect |
| 2. #22553678 | C2 | semidirect |
| 3. #22553660 | C2 | semidirect |
| 4. #22553609 | C2 | semidirect |
| 5. #22553599 | C2 | semidirect |
| 6. #22553507 | C2 | semidirect |
| 7. #22553507 | C2 | semidirect |
| 8. #22553443 | C2 | semidirect |
| 9. #22553422 | C2 | semidirect |
| 10. C4×#14523498 | C2 | semidirect |
| 11. #554×C131 | C2 | semidirect |
| 94. D4×C131 | #41 | semidirect |
| 129. C131 | #3366 | semidirect |
| 131. #554 | D131 | semidirect |
| 218. D4 | #14523514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22553984 | 2 |
| #22553678 | 2 |
| #22553660 | 2 |
| #22553609 | 2 |
| #22553599 | 2 |
| #22553507 | 2 |
| #22553443 | 2 |
| #22553422 | 2 |
| C4×#14523498 | 2 |
| #554×C131 | 2 |
| #3366 | 131 |