Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
2302 conjugacy classes of subgroups; only the 1534 normal subgroups are shown.
This group has 2302 conjugacy classes of subgroups — too many to draw. Only its 1534 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C42×C29 | C22 |
| commutator | C2 | C2×C43×C29 |
| Frattini, cosocle | C24 | C24×C29 |
| socle, prime radical | C24×C29 | C24 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C29×#376 | C4 | direct (N × H) |
| 9. C43×C29 | C4 | semidirect |
| 29. C42×C29 | C42 | semidirect |
| 30. C4×#376 | C29 | direct (N × H) |
| 50. C4×C29 | #376 | direct (N × H) |
| 54. #376 | C4×C29 | direct (N × H) |
| 56. C43 | C4×C29 | semidirect |
| 69. C29 | C4×#376 | direct (N × H) |
| 80. C42 | C42×C29 | semidirect |
| 97. C4 | C29×#376 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#376 | 2 |
| C2×C43×C29 | 2 |
| C4×C29×#95 | 2 |
| C4×#376 | 29 |