Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
326 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 90 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 | #354 |
| commutator | C42 | C22×C4×C29 |
| Frattini, cosocle | #124 | C23×C29 |
| socle | C2×C29 | C2×#354 |
| prime radical | C29×#532 | C22 |
| LCS | G ▷ C42 ▷ C2×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×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×#1414 | C2 | semidirect |
| 5. C29×#533 | C4 | semidirect |
| 7. C29×#488 | C4 | semidirect |
| 15. C2×C4×C8×C29 | C4 | semidirect |
| 83. #13602 | C29 | direct (N × H) |
| 115. #1414 | C2×C29 | semidirect |
| 132. #533 | C4×C29 | semidirect |
| 134. #488 | C4×C29 | semidirect |
| 142. C2×C4×C8 | C4×C29 | semidirect |
| 179. C29 | #13602 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3131 | 2 |
| C29×#2132 | 2 |
| C29×#2126 | 2 |
| C29×#1414 | 2 |
| #13602 | 29 |