Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
14334 conjugacy classes of subgroups; only the 7902 normal subgroups are shown.
This group has 14334 conjugacy classes of subgroups — too many to draw. Only its 7902 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C26×C29 | C22 |
| commutator | C2 | C23×C42×C29 |
| Frattini, cosocle | C23 | C25×C29 |
| LCS | G ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C26×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×C29×#95 | C2 | direct (N × H) |
| 5. C24×C4×C29 | C4 | semidirect |
| 7. C2×C29×#95 | C22 | direct (N × H) |
| 14. C23×C4×C29 | C2×C4 | semidirect |
| 16. C29×#95 | C23 | direct (N × H) |
| 26. C22×C4×C29 | C22×C4 | semidirect |
| 28. C23×#95 | C29 | direct (N × H) |
| 29. C23×C29 | #95 | direct (N × H) |
| 39. C2×C4×C29 | C23×C4 | semidirect |
| 41. C22×#95 | C2×C29 | direct (N × H) |
| 42. C22×C29 | C2×#95 | direct (N × H) |
| 52. C24×C4 | C4×C29 | semidirect |
| 54. C2×#95 | C22×C29 | direct (N × H) |
| 55. C2×C29 | C22×#95 | direct (N × H) |
| 65. C23×C4 | C2×C4×C29 | semidirect |
| 67. #95 | C23×C29 | direct (N × H) |
| 68. C29 | C23×#95 | direct (N × H) |
| 78. C22×C4 | C22×C4×C29 | semidirect |
| 80. C23 | C29×#95 | direct (N × H) |
| 90. C2×C4 | C23×C4×C29 | semidirect |
| 91. C22 | C2×C29×#95 | direct (N × H) |
| 99. C2 | C22×C29×#95 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C25×C4×C29 | 2 |
| C22×C29×#95 | 2 |
| C23×#95 | 29 |