Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
490 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#17984119 | C2 | semidirect |
| 2. C22×#14555497 | C2 | semidirect |
| 4. #22577625 | C2 | semidirect |
| 5. #22577603 | C2 | semidirect |
| 6. #22577430 | C2 | semidirect |
| 7. #22577407 | C2 | semidirect |
| 8. #22577397 | C2 | semidirect |
| 9. #519×C137 | C2 | semidirect |
| 13. C2×#14555500 | C22 | semidirect |
| 16. C2×#14555497 | C22 | semidirect |
| 23. C4⋊#11764040 | C22 | semidirect |
| 24. #17984011 | C22 | semidirect |
| 26. #17984008 | C22 | semidirect |
| 29. C4×Q8×C137 | C22 | semidirect |
| 55. C2×Q8×C137 | D4 | semidirect |
| 116. C137 | #3043 | semidirect |
| 121. #519 | D137 | semidirect |
| 142. C4×Q8 | C2×D137 | semidirect |
| 156. C2×Q8 | D548 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984119 | 2 |
| C22×#14555497 | 2 |
| #22577972 | 2 |
| #22577625 | 2 |
| #22577603 | 2 |
| #22577430 | 2 |
| #22577407 | 2 |
| #22577397 | 2 |
| #519×C137 | 2 |
| #3043 | 137 |