Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
760 conjugacy classes of subgroups; only the 407 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 407 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. C2×C4×#11764049 | C2 | direct (N × H) |
| 4. C22×#11764049 | C4 | direct (N × H) |
| 6. C4×#11764049 | C22 | direct (N × H) |
| 12. C2×#11764049 | C2×C4 | direct (N × H) |
| 14. C22×#10587739 | C8 | semidirect |
| 22. C22×Dic137 | C8 | semidirect |
| 23. C2×C4×D137 | C8 | semidirect |
| 25. C22×C4×C137 | C8 | semidirect |
| 26. #11764049 | C22×C4 | direct (N × H) |
| 28. C2×#10587739 | C2×C8 | semidirect |
| 37. C2×Dic137 | C2×C8 | semidirect |
| 38. C4×D137 | C2×C8 | semidirect |
| 41. C2×C4×C137 | C2×C8 | semidirect |
| 42. C22×C137 | C4×C8 | semidirect |
| 44. C2×D137 | C4×C8 | semidirect |
| 50. #10587739 | C22×C8 | semidirect |
| 52. C4×C137 | C22×C8 | semidirect |
| 53. Dic137 | C22×C8 | semidirect |
| 54. C2×C137 | C2×C4×C8 | semidirect |
| 56. D137 | C2×C4×C8 | semidirect |
| 59. C137 | C22×C4×C8 | semidirect |
| 81. C22×C4 | #11764049 | direct (N × H) |
| 100. C2×C4 | C2×#11764049 | direct (N × H) |
| 107. C22 | C4×#11764049 | direct (N × H) |
| 113. C4 | C22×#11764049 | direct (N × H) |
| 117. C2 | C2×C4×#11764049 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#11764049 | 2 |
| C2×C4×#11764049 | 2 |
| C22×C4×#10587739 | 2 |
| C22×C4×C8 | 137 |