Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
266 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 66 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | #353 |
| commutator | C42 | C42×C29 |
| Frattini, cosocle | #532 | C22×C29 |
| socle | C2×C29 | #1393 |
| prime radical | C29×#532 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C4×C29 ◁ C22×C4×C29 ◁ C29×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 9. C29×#355 | C4 | semidirect |
| 47. #7507 | C29 | direct (N × H) |
| 88. #355 | C4×C29 | semidirect |
| 108. C29 | #7507 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2132 | 2 |
| C29×#1963 | 2 |
| #7507 | 29 |