Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
292 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 94 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 | #1505 |
| commutator | C2×C8 | C22×C4×C29 |
| Frattini, cosocle | C2×M16 | C23×C29 |
| prime radical | C23×C29 | AGL(1,ℤ/8) |
| LCS | G ▷ C2×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C29 ◁ C2×C4×C29 ◁ C29×#405 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C29×#499 | C4 | semidirect |
| 8. C29×#494 | C4 | semidirect |
| 12. C29×#441 | C4 | semidirect |
| 76. #11771 | C29 | direct (N × H) |
| 112. #499 | C4×C29 | semidirect |
| 113. #494 | C4×C29 | semidirect |
| 117. #441 | C4×C29 | semidirect |
| 154. C29 | #11771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#3177 | 2 |
| C29×#2166 | 2 |
| C29×#1747 | 2 |
| C29×#1342 | 2 |
| C29×#1340 | 2 |
| #11771 | 29 |