Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
1112 conjugacy classes of subgroups; only the 309 normal subgroups are shown.
This group has 1112 conjugacy classes of subgroups — too many to draw. Only its 309 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×C22⋊Dic137 | C2 | semidirect |
| 2. C2×#17984003 | C2 | direct (N × H) |
| 6. C2×C22⋊Dic137 | C22 | semidirect |
| 7. #17984003 | C22 | direct (N × H) |
| 8. C25×C137 | C4 | semidirect |
| 12. C22×D4×C137 | C4 | semidirect |
| 14. C23×C4×C137 | C4 | semidirect |
| 18. C22⋊Dic137 | C23 | semidirect |
| 25. C24×C137 | C2×C4 | semidirect |
| 33. C2×D4×C137 | C2×C4 | semidirect |
| 37. C22×C4×C137 | C2×C4 | semidirect |
| 56. C23×C137 | C22×C4 | semidirect |
| 64. C2×C4×C137 | C22×C4 | semidirect |
| 77. C22×C137 | #99 | semidirect |
| 90. C2×C137 | C2×#99 | semidirect |
| 92. C137 | C22×#99 | semidirect |
| 97. C25 | Dic137 | semidirect |
| 101. C22×D4 | Dic137 | semidirect |
| 104. C23×C4 | Dic137 | semidirect |
| 114. C24 | C2×Dic137 | semidirect |
| 122. C2×D4 | C2×Dic137 | semidirect |
| 128. C22×C4 | C2×Dic137 | semidirect |
| 147. C23 | C22×Dic137 | semidirect |
| 157. C2×C4 | C22×Dic137 | semidirect |
| 170. C22 | #17984003 | direct (N × H) |
| 183. C2 | C2×#17984003 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C22⋊Dic137 | 2 |
| C2×#17984003 | 2 |
| C23×D4×C137 | 2 |
| C22×#99 | 137 |