Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
544 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 157 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 |
|---|---|---|
| 3. C2×#17984086 | C2 | semidirect |
| 5. #22577607 | C2 | direct (N × H) |
| 6. C2×#17984017 | C2 | semidirect |
| 7. C2×#17984011 | C2 | semidirect |
| 8. C2×#103×C137 | C2 | semidirect |
| 18. #17984086 | C22 | semidirect |
| 25. #17984017 | C22 | semidirect |
| 26. #17984011 | C22 | semidirect |
| 30. #103×C137 | C22 | semidirect |
| 78. C2×Dic137 | SD16 | semidirect |
| 111. Dic137 | C2×SD16 | semidirect |
| 112. C2×C137 | #461 | semidirect |
| 117. C137 | C2×#461 | semidirect |
| 126. C2×#103 | D137 | semidirect |
| 148. #103 | C2×D137 | semidirect |
| 231. C2 | #22577607 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555499 | 2 |
| C22×#14555497 | 2 |
| C2×#17984086 | 2 |
| C2×#17984050 | 2 |
| #22577607 | 2 |
| C2×#17984017 | 2 |
| C2×#17984011 | 2 |
| C2×#103×C137 | 2 |
| C2×#461 | 137 |