Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
134 conjugacy classes of subgroups; only the 62 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 62 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 | D32 |
| commutator, Frattini, cosocle | C32 | C23×C29 |
| prime radical | C2×C29×D32 | C2 |
| LCS | G ▷ C32 ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C29 ◁ C2×C4×C29 ◁ C2×C8×C29 ◁ C2×C16×C29 ◁ C2×C29×C32 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×Q64 | C2 | semidirect |
| 3. C29×SD128 | C2 | direct (N × H) |
| 4. C2×C29×C64 | C2 | semidirect |
| 8. C29×Q64 | C22 | semidirect |
| 12. C29×C64 | C22 | semidirect |
| 31. C2×SD128 | C29 | direct (N × H) |
| 41. C2×Q64 | C2×C29 | semidirect |
| 43. SD128 | C2×C29 | direct (N × H) |
| 44. C2×C64 | C2×C29 | semidirect |
| 54. Q64 | C22×C29 | semidirect |
| 58. C64 | C22×C29 | semidirect |
| 60. C2×C29 | SD128 | direct (N × H) |
| 71. C29 | C2×SD128 | direct (N × H) |
| 97. C2 | C29×SD128 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×Q64 | 2 |
| C2×C29×D32 | 2 |
| C29×SD128 | 2 |
| C2×C29×C64 | 2 |
| C2×SD128 | 29 |