Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
346 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 98 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C29 | #397 |
| commutator, Frattini, cosocle | C2×C42 | C23×C29 |
| prime radical | C2×C29×#127 | C22 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C42×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C29×#1838 | C2 | semidirect |
| 4. C29×#1286 | C2 | semidirect |
| 5. C29×#1281 | C2 | semidirect |
| 53. #10634 | C29 | direct (N × H) |
| 76. #1838 | C2×C29 | semidirect |
| 78. #1286 | C2×C29 | semidirect |
| 79. #1281 | C2×C29 | semidirect |
| 123. C29 | #10634 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1961 | 2 |
| C29×#1838 | 2 |
| C29×#1545 | 2 |
| C29×#1286 | 2 |
| C29×#1281 | 2 |
| #10634 | 29 |