Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
9486 conjugacy classes of subgroups; only the 6366 normal subgroups are shown.
This group has 9486 conjugacy classes of subgroups — too many to draw. Only its 6366 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C25×C11 | C23 |
| commutator, Frattini, cosocle | C22 | C26×C11 |
| prime radical | C26×C11 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C25×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C11×#126 | C2 | direct (N × H) |
| 2. C23×C11×C4⋊C4 | C2 | semidirect |
| 4. C23×C42×C11 | C2 | semidirect |
| 8. C2×C11×#126 | C22 | direct (N × H) |
| 9. C22×C11×C4⋊C4 | C22 | semidirect |
| 11. C22×C42×C11 | C22 | semidirect |
| 19. C11×#126 | C23 | direct (N × H) |
| 20. C2×C11×C4⋊C4 | C23 | semidirect |
| 22. C2×C42×C11 | C23 | semidirect |
| 23. C23×#126 | C11 | direct (N × H) |
| 33. C11×C4⋊C4 | C24 | semidirect |
| 35. C42×C11 | C24 | semidirect |
| 36. C22×#126 | C2×C11 | direct (N × H) |
| 37. C23×C4⋊C4 | C2×C11 | semidirect |
| 39. C23×C42 | C2×C11 | semidirect |
| 42. C23×C11 | #126 | direct (N × H) |
| 53. C2×#126 | C22×C11 | direct (N × H) |
| 54. C22×C4⋊C4 | C22×C11 | semidirect |
| 56. C22×C42 | C22×C11 | semidirect |
| 59. C22×C11 | C2×#126 | direct (N × H) |
| 71. #126 | C23×C11 | direct (N × H) |
| 72. C2×C4⋊C4 | C23×C11 | semidirect |
| 74. C2×C42 | C23×C11 | semidirect |
| 76. C2×C11 | C22×#126 | direct (N × H) |
| 87. C4⋊C4 | C24×C11 | semidirect |
| 89. C42 | C24×C11 | semidirect |
| 90. C11 | C23×#126 | direct (N × H) |
| 93. C23 | C11×#126 | direct (N × H) |
| 103. C22 | C2×C11×#126 | direct (N × H) |
| 109. C2 | C22×C11×#126 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C11×#126 | 2 |
| C23×C11×C4⋊C4 | 2 |
| C23×C11×C22⋊C4 | 2 |
| C23×C42×C11 | 2 |
| C23×#126 | 11 |