Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#17984112 | C2 | semidirect |
| 2. #22577951 | C2 | semidirect |
| 3. C4×D4×D137 | C2 | semidirect |
| 4. #22577617 | C2 | semidirect |
| 5. #22577616 | C2 | semidirect |
| 6. #22577609 | C2 | semidirect |
| 7. #22577608 | C2 | semidirect |
| 8. #22577595 | C2 | semidirect |
| 9. #22577425 | C2 | semidirect |
| 10. #22577401 | C2 | semidirect |
| 11. #459×C137 | C2 | semidirect |
| 20. #17984088 | C22 | semidirect |
| 21. #17984075 | C22 | semidirect |
| 34. C4⋊#11764040 | C22 | semidirect |
| 35. #17984017 | C22 | semidirect |
| 36. #17984013 | C22 | semidirect |
| 37. #17984011 | C22 | semidirect |
| 38. #17984009 | C22 | semidirect |
| 40. #127×C137 | C22 | semidirect |
| 42. C4⋊C8×C137 | C22 | semidirect |
| 43. #102×C137 | C22 | semidirect |
| 52. D4×D137 | D4 | semidirect |
| 145. C4×C137 | AGL(1,ℤ/8) | semidirect |
| 160. C137 | #3036 | semidirect |
| 170. #459 | D137 | semidirect |
| 183. #127 | C2×D137 | semidirect |
| 200. C4⋊C8 | C2×D137 | semidirect |
| 204. #102 | C2×D137 | semidirect |
| 311. C4 | #17984112 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984112 | 2 |
| #22577951 | 2 |
| C4×D4×D137 | 2 |
| #22577617 | 2 |
| #22577616 | 2 |
| #22577609 | 2 |
| #22577608 | 2 |
| #22577595 | 2 |
| #22577425 | 2 |
| #22577401 | 2 |
| #459×C137 | 2 |
| #3036 | 137 |