Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
270 conjugacy classes of subgroups; only the 162 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 162 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C29 |
| prime radical | C2×#41×C29 | C2 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×Q8×C29 | C2 | semidirect |
| 3. C29×C4⋊Q8 | C2 | semidirect |
| 4. C29×#124 | C2 | semidirect |
| 5. C29×#123 | C2 | semidirect |
| 6. C29×C22⋊Q8 | C2 | semidirect |
| 7. C29×#117 | C2 | semidirect |
| 48. #536 | C29 | direct (N × H) |
| 54. C22×Q8 | C2×C29 | semidirect |
| 55. C4⋊Q8 | C2×C29 | semidirect |
| 56. #124 | C2×C29 | semidirect |
| 57. #123 | C2×C29 | semidirect |
| 58. C22⋊Q8 | C2×C29 | semidirect |
| 59. #117 | C2×C29 | semidirect |
| 60. C29 | #536 | 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 |
| C22×Q8×C29 | 2 |
| C29×C4⋊Q8 | 2 |
| C29×#124 | 2 |
| C29×#123 | 2 |
| C29×C22⋊Q8 | 2 |
| C29×#117 | 2 |
| #536 | 29 |