Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
656 conjugacy classes of subgroups; only the 150 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 150 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 | #379 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C23×C29 | #120 |
| LCS | G ▷ C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C29×#564 | C4 | semidirect |
| 42. #8533 | C29 | direct (N × H) |
| 63. #564 | C4×C29 | semidirect |
| 87. C29 | #8533 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3556 | 2 |
| C29×#1994 | 2 |
| C29×#1561 | 2 |
| #8533 | 29 |