Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
2006 conjugacy classes of subgroups; only the 286 normal subgroups are shown.
This group has 2006 conjugacy classes of subgroups — too many to draw. Only its 286 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 | C2×C22⋊C4 |
| commutator | C24 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C22×C29×#127 | C2 |
| LCS | G ▷ C24 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C29 ◁ C22×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C29×#100 | C2 | semidirect |
| 3. C29×#1728 | C2 | semidirect |
| 27. C2×M16×C29 | D4 | semidirect |
| 66. #10981 | C29 | direct (N × H) |
| 85. C2×C4×C29 | #100 | semidirect |
| 95. C22×#100 | C2×C29 | semidirect |
| 96. #1728 | C2×C29 | semidirect |
| 139. C2×M16 | D4×C29 | semidirect |
| 145. C29 | #10981 | direct (N × H) |
| 197. C2×C4 | C29×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C29×#127 | 2 |
| C22×C29×#100 | 2 |
| C29×#1728 | 2 |
| #10981 | 29 |