Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
1478 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 1478 conjugacy classes of subgroups — too many to draw. Only its 166 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 | C24 | C22×C4×C29 |
| Frattini, cosocle | C23×C4 | C23×C29 |
| prime radical | C22×C29×#121 | C2 |
| LCS | G ▷ C24 ▷ 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 |
|---|---|---|
| 2. C29×#1783 | C2 | semidirect |
| 3. C29×#1463 | C2 | semidirect |
| 4. C29×#1462 | C2 | semidirect |
| 116. #8549 | C29 | direct (N × H) |
| 176. C2×C4×C29 | #100 | semidirect |
| 180. #1783 | C2×C29 | semidirect |
| 181. #1463 | C2×C29 | semidirect |
| 182. #1462 | C2×C29 | semidirect |
| 277. C29 | #8549 | direct (N × H) |
| 397. 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×#121 | 2 |
| C29×#1783 | 2 |
| C29×#1463 | 2 |
| C29×#1462 | 2 |
| #8549 | 29 |