Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
270 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 270 conjugacy classes of subgroups — too many to draw. Only its 66 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 | #1390 |
| commutator | C2×D4 | C42×C29 |
| Frattini, cosocle | #532 | C22×C29 |
| prime radical | C29×#532 | C22 |
| LCS | G ▷ C2×D4 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C22×C4×C29 ◁ C29×#532 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C29×#568 | C4 | semidirect |
| 9. C29×#410 | C4 | semidirect |
| 11. C29×#353 | C4 | semidirect |
| 14. C29×#329 | C4 | semidirect |
| 69. #7494 | C29 | direct (N × H) |
| 116. #568 | C4×C29 | semidirect |
| 121. #410 | C4×C29 | semidirect |
| 123. #353 | C4×C29 | semidirect |
| 126. #329 | C4×C29 | semidirect |
| 153. C29 | #7494 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2126 | 2 |
| C29×#1884 | 2 |
| C29×#1536 | 2 |
| #7494 | 29 |