Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
540 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 162 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 |
|---|---|---|
| 2. #22578354 | C2 | semidirect |
| 3. #22578353 | C2 | semidirect |
| 4. #22578346 | C2 | semidirect |
| 5. #22578345 | C2 | semidirect |
| 6. C4×C4⋊#10587739 | C2 | semidirect |
| 7. #22578339 | C2 | semidirect |
| 22. C4×D548 | C4 | semidirect |
| 23. D4×Dic137 | C4 | semidirect |
| 24. #17984050 | C4 | semidirect |
| 25. C4×C22⋊D137 | C4 | semidirect |
| 26. #17984048 | C4 | semidirect |
| 30. C4×D4×C137 | C4 | semidirect |
| 132. C137 | #2319 | semidirect |
| 149. C4×D4 | #10587739 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578355 | 2 |
| #22578354 | 2 |
| #22578353 | 2 |
| #22578346 | 2 |
| #22578345 | 2 |
| C4×C4⋊#10587739 | 2 |
| #22578339 | 2 |
| C4×D4×D137 | 2 |
| #2319 | 137 |