Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1258 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 1258 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C29 | #120 |
| commutator | C23 | C2×C42×C29 |
| Frattini, cosocle | C25 | C23×C29 |
| prime radical | C25×C29 | C23 |
| LCS | G ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C25×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C29×#381 | C4 | semidirect |
| 51. C22×C4×C29 | C42 | semidirect |
| 59. #10936 | C29 | direct (N × H) |
| 111. #381 | C4×C29 | semidirect |
| 138. C29 | #10936 | direct (N × H) |
| 160. C22×C4 | C42×C29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#381 | 2 |
| C29×#2273 | 2 |
| C2×C29×#342 | 2 |
| #10936 | 29 |