Finite Group DatabasebetaFinite Group DatabasebetaOrder 2816.
4126 conjugacy classes of subgroups; only the 2795 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2795 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C22×#66867 | C2 | direct (N × H) |
| 8. C23×C11⋊C8 | C4 | semidirect |
| 10. C2×#66867 | C22 | direct (N × H) |
| 19. C22×C11⋊C8 | C2×C4 | semidirect |
| 21. #66867 | C23 | direct (N × H) |
| 34. C2×C11⋊C8 | C22×C4 | semidirect |
| 39. C23×C11 | #97 | semidirect |
| 49. C11⋊C8 | C23×C4 | semidirect |
| 57. C22×C11 | C2×#97 | semidirect |
| 75. C2×C11 | C22×#97 | semidirect |
| 91. C11 | C23×#97 | semidirect |
| 92. C23 | #66867 | direct (N × H) |
| 103. C22 | C2×#66867 | direct (N × H) |
| 110. C2 | C22×#66867 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×C11⋊C8 | 2 |
| C22×#66867 | 2 |
| C23×C42×C11 | 2 |
| C23×#97 | 11 |