Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
3294 conjugacy classes of subgroups; only the 974 normal subgroups are shown.
This group has 3294 conjugacy classes of subgroups — too many to draw. Only its 974 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, Frattini, cosocle | C23 | C25×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 |
|---|---|---|
| 1. C29×#2842 | C2 | direct (N × H) |
| 2. C2×C29×#399 | C2 | semidirect |
| 3. C2×C29×#396 | C2 | semidirect |
| 6. C22×C4⋊C4×C29 | C22 | semidirect |
| 9. C29×#399 | C22 | semidirect |
| 10. C29×#396 | C22 | semidirect |
| 12. C2×C29×#95 | C22 | semidirect |
| 20. C2×C4⋊C4×C29 | C23 | semidirect |
| 25. C29×#95 | C23 | semidirect |
| 43. C2×#2842 | C29 | direct (N × H) |
| 61. #2842 | C2×C29 | direct (N × H) |
| 62. C2×#399 | C2×C29 | semidirect |
| 63. C2×#396 | C2×C29 | semidirect |
| 78. C22×C4⋊C4 | C22×C29 | semidirect |
| 81. #399 | C22×C29 | semidirect |
| 82. #396 | C22×C29 | semidirect |
| 84. C2×#95 | C22×C29 | semidirect |
| 87. C2×C29 | #2842 | direct (N × H) |
| 97. C2×C4⋊C4 | C23×C29 | semidirect |
| 102. #95 | C23×C29 | semidirect |
| 103. C29 | C2×#2842 | direct (N × H) |
| 152. C2 | C29×#2842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C29×#2842 | 2 |
| C2×C29×#399 | 2 |
| C2×C29×#396 | 2 |
| C2×C29×#379 | 2 |
| C2×#2842 | 29 |