Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
3246 conjugacy classes of subgroups; only the 542 normal subgroups are shown.
This group has 3246 conjugacy classes of subgroups — too many to draw. Only its 542 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C29 | C24 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C24 | C24×C29 |
| prime radical | C26×C29 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C29×#1440 | C2 | semidirect |
| 4. C29×C22⋊#95 | C2 | semidirect |
| 8. C22×C22⋊C4×C29 | C4 | semidirect |
| 13. C2×C29×#95 | C22 | semidirect |
| 60. #14341 | C29 | direct (N × H) |
| 91. #1440 | C2×C29 | semidirect |
| 92. C22⋊#95 | C2×C29 | semidirect |
| 113. C22×C22⋊C4 | C4×C29 | semidirect |
| 118. C2×#95 | C22×C29 | semidirect |
| 144. C29 | #14341 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊C4×C29 | 2 |
| C2×C29×#379 | 2 |
| C29×#1440 | 2 |
| C29×C22⋊#95 | 2 |
| #14341 | 29 |