Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
196 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 50 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 | #327 |
| commutator | C22×C8 | C2×C4×C29 |
| Frattini, cosocle | C2×C22⋊C8 | C22×C29 |
| prime radical | C24×C29 | SD16 |
| LCS | G ▷ C22×C8 ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C29×C22⋊C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 46. #7085 | C29 | direct (N × H) |
| 116. C29 | #7085 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2076 | 2 |
| C29×#1314 | 2 |
| C29×#1293 | 2 |
| #7085 | 29 |