Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
490 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 141 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×#17984118 | C2 | semidirect |
| 2. C22×#14555498 | C2 | semidirect |
| 3. #22577880 | C2 | semidirect |
| 4. #22577622 | C2 | semidirect |
| 5. #22577600 | C2 | semidirect |
| 6. #22577430 | C2 | semidirect |
| 7. #22577408 | C2 | semidirect |
| 8. #22577399 | C2 | semidirect |
| 12. C2×#14555500 | C22 | semidirect |
| 15. C2×#14555498 | C22 | semidirect |
| 18. C4×Dic274 | C22 | semidirect |
| 22. C4⋊#11764040 | C22 | semidirect |
| 23. #17984012 | C22 | semidirect |
| 25. #17984009 | C22 | semidirect |
| 35. C2×Dic274 | D4 | semidirect |
| 116. C137 | #3043 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984118 | 2 |
| C22×#14555498 | 2 |
| #22577880 | 2 |
| #22577622 | 2 |
| #22577600 | 2 |
| #22577430 | 2 |
| #22577408 | 2 |
| #22577399 | 2 |
| #535×C137 | 2 |
| #3043 | 137 |