Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1118 conjugacy classes of subgroups; only the 622 normal subgroups are shown.
This group has 1118 conjugacy classes of subgroups — too many to draw. Only its 622 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C29 | C24 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C22×C4 | C24×C29 |
| socle | C23×C29 | C23×C4 |
| prime radical | C24×C29 | C22×C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1843 | C2 | semidirect |
| 34. #20792 | C29 | direct (N × H) |
| 49. #1843 | C2×C29 | semidirect |
| 78. C29 | #20792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#423 | 2 |
| C2×C29×#376 | 2 |
| C29×#1843 | 2 |
| #20792 | 29 |