Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
608 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 197 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×D4×Dic137 | C2 | semidirect |
| 3. C2×#17984050 | C2 | semidirect |
| 4. #22577512 | C2 | direct (N × H) |
| 5. C2×#17984019 | C2 | semidirect |
| 6. C2×#17984010 | C2 | semidirect |
| 7. C2×#17983998 | C2 | semidirect |
| 8. C2×#102×C137 | C2 | semidirect |
| 12. C2×#14555495 | C4 | semidirect |
| 16. D4×Dic137 | C22 | semidirect |
| 18. #17984050 | C22 | semidirect |
| 23. #17984019 | C22 | semidirect |
| 24. #17984010 | C22 | semidirect |
| 25. #17983998 | C22 | semidirect |
| 29. #102×C137 | C22 | semidirect |
| 33. C2×D548 | C2×C4 | semidirect |
| 42. #14555495 | C2×C4 | semidirect |
| 43. C2×#11764040 | C2×C4 | semidirect |
| 54. C2×D4×C137 | C2×C4 | semidirect |
| 68. D548 | C22×C4 | semidirect |
| 77. #11764040 | C22×C4 | semidirect |
| 85. D4×C137 | C22×C4 | semidirect |
| 113. C2×C137 | #442 | semidirect |
| 118. C137 | C2×#442 | semidirect |
| 126. C2×#102 | D137 | semidirect |
| 147. #102 | C2×D137 | semidirect |
| 157. C2×D4 | C4×D137 | semidirect |
| 195. D4 | C2×C4×D137 | semidirect |
| 233. C2 | #22577512 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14555495 | 2 |
| C2×D4×Dic137 | 2 |
| C2×#17984050 | 2 |
| #22577512 | 2 |
| C2×#17984019 | 2 |
| C2×#17984010 | 2 |
| C2×#17983998 | 2 |
| C2×#102×C137 | 2 |
| C2×#442 | 137 |