Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
564 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 564 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. C22×#14555497 | C2 | semidirect |
| 3. C2×#17984077 | C2 | semidirect |
| 4. C2×#17984050 | C2 | semidirect |
| 5. #22577621 | C2 | direct (N × H) |
| 6. C2×#17984017 | C2 | semidirect |
| 7. C2×#17984008 | C2 | semidirect |
| 8. C2×#103×C137 | C2 | semidirect |
| 13. C2×#14555497 | C22 | semidirect |
| 18. #17984077 | C22 | semidirect |
| 20. #17984050 | C22 | semidirect |
| 25. #17984017 | C22 | semidirect |
| 26. #17984008 | C22 | semidirect |
| 30. #103×C137 | C22 | semidirect |
| 117. C2×C137 | #463 | semidirect |
| 123. C137 | C2×#463 | semidirect |
| 131. C2×#103 | D137 | semidirect |
| 153. #103 | C2×D137 | semidirect |
| 243. C2 | #22577621 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555497 | 2 |
| C22×D1096 | 2 |
| C2×#17984077 | 2 |
| C2×#17984050 | 2 |
| #22577621 | 2 |
| C2×#17984017 | 2 |
| C2×#17984008 | 2 |
| C2×#103×C137 | 2 |
| C2×#463 | 137 |