Finite Group DatabasebetaFinite Group DatabasebetaOrder 1088.
298 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 111 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×#63252 | C2 | semidirect |
| 2. C22×D68 | C2 | semidirect |
| 3. C2×M16×C17 | C2 | semidirect |
| 4. #10587594 | C2 | direct (N × H) |
| 5. C2×D136 | C2 | semidirect |
| 6. C2×#63219 | C2 | semidirect |
| 11. #63252 | C22 | semidirect |
| 15. C2×D68 | C22 | semidirect |
| 16. C2×D68 | C22 | semidirect |
| 18. C2×Dic34 | C22 | semidirect |
| 19. M16×C17 | C22 | semidirect |
| 20. C2×C8×C17 | C22 | semidirect |
| 21. D136 | C22 | semidirect |
| 22. #63219 | C22 | semidirect |
| 38. D68 | C23 | semidirect |
| 41. Dic34 | C23 | semidirect |
| 42. C8×C17 | C23 | semidirect |
| 57. C2×C17 | AGL(1,ℤ/8) | semidirect |
| 66. C2×M16 | D17 | semidirect |
| 67. C17 | C2×AGL(1,ℤ/8) | semidirect |
| 82. M16 | C2×D17 | semidirect |
| 83. C2×C8 | C2×D17 | semidirect |
| 103. C8 | C22×D17 | semidirect |
| 119. C2 | #10587594 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#63252 | 2 |
| C22×D68 | 2 |
| C2×M16×C17 | 2 |
| #10587594 | 2 |
| C2×D136 | 2 |
| C2×#63219 | 2 |
| C2×AGL(1,ℤ/8) | 17 |