Finite Group DatabasebetaFinite Group DatabasebetaOrder 7424.
466 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C29 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C24×C29 |
| socle | C2×C29 | C22×D16 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C29 ◁ C22×C4×C29 ◁ C22×C8×C29 ◁ C22×C16×C29 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C29×#508 | C2 | semidirect |
| 2. C29×#2264 | C2 | semidirect |
| 3. C29×#2263 | C2 | semidirect |
| 4. C29×#2262 | C2 | semidirect |
| 5. C2×C29×M64 | C2 | semidirect |
| 10. C29×#508 | C22 | semidirect |
| 11. C2×C29×Q32 | C22 | semidirect |
| 13. C2×C29×D16 | C22 | semidirect |
| 15. C29×Q64 | C22 | semidirect |
| 16. C29×SD64 | C22 | semidirect |
| 17. C29×D32 | C22 | semidirect |
| 18. C29×M64 | C22 | semidirect |
| 19. C2×C29×C32 | C22 | semidirect |
| 62. #33981 | C29 | direct (N × H) |
| 81. C2×#508 | C2×C29 | semidirect |
| 82. #2264 | C2×C29 | semidirect |
| 83. #2263 | C2×C29 | semidirect |
| 84. #2262 | C2×C29 | semidirect |
| 85. C2×M64 | C2×C29 | semidirect |
| 99. #508 | C22×C29 | semidirect |
| 100. C2×Q32 | C22×C29 | semidirect |
| 102. C2×D16 | C22×C29 | semidirect |
| 104. Q64 | C22×C29 | semidirect |
| 105. SD64 | C22×C29 | semidirect |
| 106. D32 | C22×C29 | semidirect |
| 107. M64 | C22×C29 | semidirect |
| 108. C2×C32 | C22×C29 | semidirect |
| 133. C29 | #33981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C29×#508 | 2 |
| C29×#2264 | 2 |
| C29×#2263 | 2 |
| C29×#2262 | 2 |
| C2×C29×M64 | 2 |
| #33981 | 29 |