Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
526 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #353 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | #127 | C23×C29 |
| prime radical | C2×C29×#493 | C2 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C29 ◁ C22×C4×C29 ◁ C2×C29×#127 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#353 | C2 | semidirect |
| 3. C29×#1408 | C2 | direct (N × H) |
| 5. C2×C29×#127 | C4 | semidirect |
| 8. C29×#493 | C4 | semidirect |
| 11. C2×C4×C8×C29 | C4 | semidirect |
| 13. C29×#353 | C22 | semidirect |
| 27. C29×#127 | C2×C4 | semidirect |
| 35. C4×C8×C29 | C2×C4 | semidirect |
| 67. C2×#1408 | C29 | direct (N × H) |
| 99. C2×#353 | C2×C29 | semidirect |
| 100. #1408 | C2×C29 | direct (N × H) |
| 121. C2×#127 | C4×C29 | semidirect |
| 124. #493 | C4×C29 | semidirect |
| 127. C2×C4×C8 | C4×C29 | semidirect |
| 129. #353 | C22×C29 | semidirect |
| 135. C2×C29 | #1408 | direct (N × H) |
| 150. #127 | C2×C4×C29 | semidirect |
| 158. C4×C8 | C2×C4×C29 | semidirect |
| 159. C29 | C2×#1408 | direct (N × H) |
| 245. C2 | C29×#1408 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#493 | 2 |
| C2×C29×#353 | 2 |
| C29×#1408 | 2 |
| C2×#1408 | 29 |