Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
656 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 145 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. C2×#17984115 | C2 | semidirect |
| 2. #22577954 | C2 | semidirect |
| 3. #127×D137 | C2 | semidirect |
| 4. #22577789 | C2 | semidirect |
| 5. #22577780 | C2 | semidirect |
| 6. #22577779 | C2 | semidirect |
| 7. #22577777 | C2 | semidirect |
| 8. C4×#14555493 | C2 | semidirect |
| 9. #492×C137 | C2 | semidirect |
| 14. C2×#14555497 | C22 | semidirect |
| 15. C2×D1096 | C22 | semidirect |
| 16. C2×#14555495 | C22 | semidirect |
| 19. #17984085 | C22 | semidirect |
| 22. #17984077 | C22 | semidirect |
| 26. #17983998 | C22 | semidirect |
| 27. C4×#11764040 | C22 | semidirect |
| 28. C2×SD16×C137 | C22 | semidirect |
| 29. C4⋊Q8×C137 | C22 | semidirect |
| 31. C4×C8×C137 | C22 | semidirect |
| 49. #14555493 | D4 | semidirect |
| 78. #11764040 | C2×D4 | semidirect |
| 86. C8×C137 | C2×D4 | semidirect |
| 98. C4×C137 | AGL(1,ℤ/8) | semidirect |
| 108. C137 | #3151 | semidirect |
| 117. #492 | D137 | semidirect |
| 124. C2×SD16 | C2×D137 | semidirect |
| 128. C4⋊Q8 | C2×D137 | semidirect |
| 140. C4×C8 | C2×D137 | semidirect |
| 195. C8 | D4×D137 | semidirect |
| 209. C4 | #17984115 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984115 | 2 |
| #22577954 | 2 |
| #127×D137 | 2 |
| #22577789 | 2 |
| #22577780 | 2 |
| #22577779 | 2 |
| #22577777 | 2 |
| C4×#14555493 | 2 |
| #492×C137 | 2 |
| #3151 | 137 |