Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#17984119 | C2 | semidirect |
| 3. C2×#17984077 | C2 | semidirect |
| 4. #22577871 | C2 | semidirect |
| 5. #22577628 | C2 | semidirect |
| 6. #22577621 | C2 | semidirect |
| 7. #22577426 | C2 | semidirect |
| 8. #22577407 | C2 | semidirect |
| 9. #419×C137 | C2 | semidirect |
| 14. C2×#14555500 | C22 | semidirect |
| 16. C2×#14555497 | C22 | semidirect |
| 22. #17984053 | C22 | semidirect |
| 23. #17984050 | C22 | semidirect |
| 29. #17984017 | C22 | semidirect |
| 34. #103×C137 | C22 | semidirect |
| 125. C137 | #3040 | semidirect |
| 134. #419 | D137 | semidirect |
| 159. #103 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984119 | 2 |
| C2×#17984116 | 2 |
| C2×#17984077 | 2 |
| #22577871 | 2 |
| #22577628 | 2 |
| #22577621 | 2 |
| #22577426 | 2 |
| #22577407 | 2 |
| #419×C137 | 2 |
| #3040 | 137 |