Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
180 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 180 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 | C4×C29 | H(3,ℤ/4) |
| commutator | C2×C8 | C42×C29 |
| Frattini, cosocle | C4×M16 | C22×C29 |
| socle | C2×C29 | #1288 |
| prime radical | C23×C29 | #104 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 8. C29×#347 | C4 | semidirect |
| 14. C29×#322 | C4 | semidirect |
| 15. C82×C29 | C4 | semidirect |
| 50. #7226 | C29 | direct (N × H) |
| 83. #347 | C4×C29 | semidirect |
| 89. #322 | C4×C29 | semidirect |
| 90. C82 | C4×C29 | semidirect |
| 108. C29 | #7226 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2165 | 2 |
| C29×#1841 | 2 |
| C29×#1453 | 2 |
| #7226 | 29 |