Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
5990 conjugacy classes of subgroups; only the 750 normal subgroups are shown.
This group has 5990 conjugacy classes of subgroups — too many to draw. Only its 750 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4×C29 | C24 |
| commutator | C23 | C23×C4×C29 |
| Frattini, cosocle | C22×C4 | C24×C29 |
| socle | C23×C29 | C23×C4 |
| prime radical | C26×C29 | C4 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C22×C4×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C29×#407 | C2 | semidirect |
| 3. C29×#1779 | C2 | semidirect |
| 10. C22×M16×C29 | C22 | semidirect |
| 12. C2×C29×C22⋊C8 | C22 | semidirect |
| 30. C22×C8×C29 | C23 | semidirect |
| 39. C24×C29 | M16 | semidirect |
| 60. #20579 | C29 | direct (N × H) |
| 86. C2×#407 | C2×C29 | semidirect |
| 87. #1779 | C2×C29 | semidirect |
| 95. C22×C29 | #407 | semidirect |
| 107. C22×M16 | C22×C29 | semidirect |
| 109. C2×C22⋊C8 | C22×C29 | semidirect |
| 131. C22×C8 | C23×C29 | semidirect |
| 133. C29 | #20579 | direct (N × H) |
| 141. C24 | M16×C29 | semidirect |
| 193. C22 | C29×#407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4×C29 | 2 |
| C2×C29×#407 | 2 |
| C29×#1779 | 2 |
| #20579 | 29 |