Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
286 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 286 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 | C22×C29 | #340 |
| commutator | C2×C8 | C42×C29 |
| Frattini, cosocle | C23×C8 | C22×C29 |
| prime radical | C24×C29 | SD16 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C23×C4×C29 ◁ C23×C8×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×C29×M32 | C4 | semidirect |
| 12. C29×#341 | C4 | semidirect |
| 59. #7235 | C29 | direct (N × H) |
| 111. C2×M32 | C4×C29 | semidirect |
| 118. #341 | C4×C29 | semidirect |
| 145. C29 | #7235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2112 | 2 |
| C29×#1810 | 2 |
| C29×#1808 | 2 |
| #7235 | 29 |