Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
266 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 266 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×#41×C29 | C2 | semidirect |
| 2. C2×#90805 | C2 | semidirect |
| 3. #11745312 | C2 | direct (N × H) |
| 4. C2×#90785 | C2 | semidirect |
| 5. C2×#90784 | C2 | semidirect |
| 6. C2×#90783 | C2 | semidirect |
| 7. C2×#90782 | C2 | semidirect |
| 8. C22×#6597 | C2 | semidirect |
| 10. #41×C29 | C22 | semidirect |
| 18. #90805 | C22 | semidirect |
| 22. #90785 | C22 | semidirect |
| 23. #90784 | C22 | semidirect |
| 24. #90783 | C22 | semidirect |
| 25. #90782 | C22 | semidirect |
| 28. C2×#6597 | C22 | semidirect |
| 67. C2×C29 | #135 | semidirect |
| 71. C2×#41 | D29 | semidirect |
| 78. C29 | C2×#135 | semidirect |
| 82. #41 | C2×D29 | semidirect |
| 137. C2 | #11745312 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C29 | 2 |
| C2×#90805 | 2 |
| #11745312 | 2 |
| C2×#90785 | 2 |
| C2×#90784 | 2 |
| C2×#90783 | 2 |
| C2×#90782 | 2 |
| C22×#6597 | 2 |
| C2×#135 | 29 |