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. C22×D4×C17 | C2 | semidirect |
| 2. C2×#63252 | C2 | semidirect |
| 3. C2×#63229 | C2 | semidirect |
| 4. #10587618 | C2 | direct (N × H) |
| 5. C2×#63228 | C2 | semidirect |
| 6. C2×#63223 | C2 | semidirect |
| 11. C2×D4×C17 | C22 | semidirect |
| 15. #63252 | C22 | semidirect |
| 16. C2×D68 | C22 | semidirect |
| 18. C2×Dic34 | C22 | semidirect |
| 19. #63229 | C22 | semidirect |
| 20. #63228 | C22 | semidirect |
| 21. #63223 | C22 | semidirect |
| 22. C2×#3622 | C22 | semidirect |
| 38. D68 | C23 | semidirect |
| 41. Dic34 | C23 | semidirect |
| 42. #3622 | C23 | semidirect |
| 58. C2×C17 | AGL(1,ℤ/8) | semidirect |
| 62. C22×D4 | D17 | semidirect |
| 67. C17 | C2×AGL(1,ℤ/8) | semidirect |
| 77. C2×D4 | C2×D17 | semidirect |
| 119. C2 | #10587618 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×C17 | 2 |
| C2×#63252 | 2 |
| C2×#63229 | 2 |
| #10587618 | 2 |
| C2×#63228 | 2 |
| C2×#63223 | 2 |
| C2×AGL(1,ℤ/8) | 17 |