Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
420 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 126 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 | #410 |
| commutator | C22×C4 | C22×C4×C29 |
| Frattini, cosocle | C2×#41 | C23×C29 |
| socle | C2×C29 | #1799 |
| prime radical | C29×#532 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C2×C8×C29 ◁ C2×C29×#131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1813 | C2 | semidirect |
| 4. C29×#1392 | C2 | semidirect |
| 84. #12809 | C29 | direct (N × H) |
| 116. #1813 | C2×C29 | semidirect |
| 117. #1392 | C2×C29 | semidirect |
| 179. C29 | #12809 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2931 | 2 |
| C29×#2132 | 2 |
| C29×#1813 | 2 |
| C29×#1392 | 2 |
| #12809 | 29 |