Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
180 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 180 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 | #354 |
| commutator | C42 | C2×C8×C29 |
| Frattini, cosocle | #384 | C22×C29 |
| prime radical | C23×C29 | #99 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C29 ◁ C22×C4×C29 ◁ C29×#384 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 11. C29×#125 | C8 | semidirect |
| 36. #7358 | C29 | direct (N × H) |
| 79. #125 | C8×C29 | semidirect |
| 87. C29 | #7358 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1992 | 2 |
| C29×#1325 | 2 |
| #7358 | 29 |