Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
418 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 110 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 | #381 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C24×C29 | C2×D4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 10. C4×C4⋊C4×C29 | C4 | semidirect |
| 12. C29×#376 | C4 | semidirect |
| 13. C43×C29 | C4 | semidirect |
| 56. #8741 | C29 | direct (N × H) |
| 101. C4×C4⋊C4 | C4×C29 | semidirect |
| 103. #376 | C4×C29 | semidirect |
| 104. C43 | C4×C29 | semidirect |
| 129. C29 | #8741 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2298 | 2 |
| C29×#1822 | 2 |
| C29×#1820 | 2 |
| C29×#1284 | 2 |
| #8741 | 29 |