Finite Group DatabasebetaFinite Group DatabasebetaOrder 1856.
124 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 54 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 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C29 |
| prime radical | C2×D8×C29 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×SD16×C29 | C2 | semidirect |
| 3. C29×#124 | C2 | semidirect |
| 4. C4×D4×C29 | C2 | semidirect |
| 5. C29×C4⋊C8 | C2 | semidirect |
| 6. C29×#103 | C2 | semidirect |
| 7. C29×#102 | C2 | semidirect |
| 50. #463 | C29 | direct (N × H) |
| 56. C2×SD16 | C2×C29 | semidirect |
| 58. #124 | C2×C29 | semidirect |
| 59. C4×D4 | C2×C29 | semidirect |
| 60. C4⋊C8 | C2×C29 | semidirect |
| 61. #103 | C2×C29 | semidirect |
| 62. #102 | C2×C29 | semidirect |
| 63. C29 | #463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×SD16×C29 | 2 |
| C2×D8×C29 | 2 |
| C29×#124 | 2 |
| C4×D4×C29 | 2 |
| C29×C4⋊C8 | 2 |
| C29×#103 | 2 |
| C29×#102 | 2 |
| #463 | 29 |