Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #22577769 | C2 | semidirect |
| 3. #22577765 | C2 | semidirect |
| 4. #22577760 | C2 | semidirect |
| 5. #22577751 | C2 | semidirect |
| 6. #22577407 | C2 | semidirect |
| 7. #22577402 | C2 | semidirect |
| 8. #22577397 | C2 | semidirect |
| 9. C2×#17984008 | C2 | semidirect |
| 10. #22577359 | C2 | semidirect |
| 11. #544×C137 | C2 | semidirect |
| 21. #17984011 | C22 | semidirect |
| 22. #17984011 | C22 | semidirect |
| 23. #17984011 | C22 | semidirect |
| 28. #17984008 | C22 | semidirect |
| 29. #17984008 | C22 | semidirect |
| 30. #17984008 | C22 | semidirect |
| 31. #17983999 | C22 | semidirect |
| 32. C4×#11764040 | C22 | semidirect |
| 34. C4⋊Q8×C137 | C22 | semidirect |
| 36. #125×C137 | C22 | semidirect |
| 135. C137 | #3136 | semidirect |
| 137. #544 | D137 | semidirect |
| 153. C4⋊Q8 | C2×D137 | semidirect |
| 156. #125 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22577972 | 2 |
| #22577769 | 2 |
| #22577765 | 2 |
| #22577760 | 2 |
| #22577751 | 2 |
| #22577407 | 2 |
| #22577402 | 2 |
| #22577397 | 2 |
| C2×#17984008 | 2 |
| #22577359 | 2 |
| #544×C137 | 2 |
| #3136 | 137 |