Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
342 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 342 conjugacy classes of subgroups — too many to draw. Only its 78 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 | #342 |
| commutator | C24 | C42×C29 |
| Frattini, cosocle | C2×C4×D4 | C22×C29 |
| prime radical | C22×D4×C29 | C2×C4 |
| LCS | G ▷ C24 ▷ C23 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C22×C4×C29 ◁ C2×C4×D4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C22×M16×C29 | C4 | semidirect |
| 9. C2×C29×C22⋊C8 | C4 | semidirect |
| 14. C29×#323 | C4 | semidirect |
| 75. #7320 | C29 | direct (N × H) |
| 143. C22×M16 | C4×C29 | semidirect |
| 148. C2×C22⋊C8 | C4×C29 | semidirect |
| 153. #323 | C4×C29 | semidirect |
| 184. C29 | #7320 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#1870 | 2 |
| C29×#1799 | 2 |
| C29×#1466 | 2 |
| #7320 | 29 |