Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
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×C11 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C11 |
| prime radical | C26×C11 | C22 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C11 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C11×#2842 | C2 | direct (N × H) |
| 2. C2×C11×#399 | C2 | semidirect |
| 3. C2×C11×#396 | C2 | semidirect |
| 6. C22×C11×C4⋊C4 | C22 | semidirect |
| 9. C11×#399 | C22 | semidirect |
| 10. C11×#396 | C22 | semidirect |
| 12. C2×C11×#95 | C22 | semidirect |
| 20. C2×C11×C4⋊C4 | C23 | semidirect |
| 25. C11×#95 | C23 | semidirect |
| 26. C2×#2842 | C11 | direct (N × H) |
| 44. #2842 | C2×C11 | direct (N × H) |
| 45. C2×#399 | C2×C11 | semidirect |
| 46. C2×#396 | C2×C11 | semidirect |
| 66. C22×C4⋊C4 | C22×C11 | semidirect |
| 69. #399 | C22×C11 | semidirect |
| 70. #396 | C22×C11 | semidirect |
| 72. C2×#95 | C22×C11 | semidirect |
| 92. C2×C4⋊C4 | C23×C11 | semidirect |
| 97. #95 | C23×C11 | semidirect |
| 100. C2×C11 | #2842 | direct (N × H) |
| 120. C11 | C2×#2842 | direct (N × H) |
| 152. C2 | C11×#2842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C11×#2842 | 2 |
| C2×C11×#399 | 2 |
| C2×C11×#396 | 2 |
| C2×C11×#379 | 2 |
| C2×#2842 | 11 |