Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
714 conjugacy classes of subgroups; only the 138 normal subgroups are shown.
This group has 714 conjugacy classes of subgroups — too many to draw. Only its 138 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C29 | #1782 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C22×D4 | C23×C29 |
| prime radical | C29×#535 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C23×C29 ◁ C29×#518 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×C29×#354 | C2 | semidirect |
| 4. C29×#1828 | C2 | semidirect |
| 9. C29×#536 | C4 | semidirect |
| 11. C29×#533 | C4 | semidirect |
| 14. C29×#519 | C4 | semidirect |
| 16. C4×#41×C29 | C4 | semidirect |
| 116. #12728 | C29 | direct (N × H) |
| 150. C2×#354 | C2×C29 | semidirect |
| 151. #1828 | C2×C29 | semidirect |
| 174. #536 | C4×C29 | semidirect |
| 176. #533 | C4×C29 | semidirect |
| 179. #519 | C4×C29 | semidirect |
| 181. C4×#41 | C4×C29 | semidirect |
| 238. C29 | #12728 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3510 | 2 |
| C29×#2127 | 2 |
| C2×C29×#354 | 2 |
| C29×#1828 | 2 |
| #12728 | 29 |