Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
298 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 103 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×#63256 | C2 | semidirect |
| 2. C2×D4×D17 | C2 | semidirect |
| 3. C2×SD16×C17 | C2 | semidirect |
| 4. C2×#63230 | C2 | semidirect |
| 5. C2×#63228 | C2 | semidirect |
| 6. #10587600 | C2 | direct (N × H) |
| 7. C2×D136 | C2 | semidirect |
| 8. C2×#63218 | C2 | semidirect |
| 10. C2×Q8×C17 | C22 | semidirect |
| 14. #63256 | C22 | semidirect |
| 16. D4×D17 | C22 | semidirect |
| 19. C2×D68 | C22 | semidirect |
| 22. SD16×C17 | C22 | semidirect |
| 23. C2×C8×C17 | C22 | semidirect |
| 24. #63230 | C22 | semidirect |
| 25. #63228 | C22 | semidirect |
| 26. C2×#3622 | C22 | semidirect |
| 27. D136 | C22 | semidirect |
| 28. #63218 | C22 | semidirect |
| 36. Q8×C17 | C23 | semidirect |
| 47. D68 | C23 | semidirect |
| 51. C8×C17 | C23 | semidirect |
| 52. #3622 | C23 | semidirect |
| 69. C2×C17 | AGL(1,ℤ/8) | semidirect |
| 78. C2×SD16 | D17 | semidirect |
| 82. C17 | C2×AGL(1,ℤ/8) | semidirect |
| 86. C2×Q8 | C2×D17 | semidirect |
| 97. SD16 | C2×D17 | semidirect |
| 102. C2×C8 | C2×D17 | semidirect |
| 110. Q8 | C22×D17 | semidirect |
| 126. C8 | C22×D17 | semidirect |
| 145. C2 | #10587600 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63256 | 2 |
| C2×D4×D17 | 2 |
| C2×SD16×C17 | 2 |
| C2×#63230 | 2 |
| C2×#63228 | 2 |
| #10587600 | 2 |
| C2×D136 | 2 |
| C2×#63218 | 2 |
| C2×AGL(1,ℤ/8) | 17 |