Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
266 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 266 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×#90809 | C2 | semidirect |
| 2. C2×#90807 | C2 | semidirect |
| 3. C2×SD16×C29 | C2 | semidirect |
| 4. C2×#90785 | C2 | semidirect |
| 5. C2×#90782 | C2 | semidirect |
| 6. #11745278 | C2 | direct (N × H) |
| 7. C2×#90773 | C2 | semidirect |
| 8. C2×C8×D29 | C2 | semidirect |
| 14. #90809 | C22 | semidirect |
| 16. #90807 | C22 | semidirect |
| 22. SD16×C29 | C22 | semidirect |
| 24. #90785 | C22 | semidirect |
| 25. #90782 | C22 | semidirect |
| 27. #90773 | C22 | semidirect |
| 28. C8×D29 | C22 | semidirect |
| 66. C2×C29 | #135 | semidirect |
| 75. C2×SD16 | D29 | semidirect |
| 78. C29 | C2×#135 | semidirect |
| 94. SD16 | C2×D29 | semidirect |
| 137. C2 | #11745278 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90809 | 2 |
| C2×#90807 | 2 |
| C2×SD16×C29 | 2 |
| C2×#90785 | 2 |
| C2×#90782 | 2 |
| #11745278 | 2 |
| C2×#90773 | 2 |
| C2×C8×D29 | 2 |
| C2×#135 | 29 |