Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
728 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 103 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 |
|---|---|---|
| 3. #19134878 | C2 | semidirect |
| 4. #19134807 | C2 | semidirect |
| 5. #19132719 | C2 | semidirect |
| 6. #19132714 | C2 | semidirect |
| 27. C43×AΣL(1,𝔽16) | C4 | semidirect |
| 72. #100×C43 | C2×C4 | semidirect |
| 74. #99×C43 | C2×C4 | semidirect |
| 81. C24×C43 | C4⋊C4 | semidirect |
| 122. C22⋊C4×C43 | C4⋊C4 | semidirect |
| 290. AΣL(1,𝔽16) | Dic43 | semidirect |
| 294. C43 | #12958 | semidirect |
| 333. #100 | C2×Dic43 | semidirect |
| 337. #99 | C2×Dic43 | semidirect |
| 348. C24 | C4⋊Dic43 | semidirect |
| 407. C22⋊C4 | C4⋊Dic43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19137579 | 2 |
| #19135004 | 2 |
| #19134878 | 2 |
| #19134807 | 2 |
| #19132719 | 2 |
| #19132714 | 2 |
| C2×C43×AΣL(1,𝔽16) | 2 |
| #12958 | 43 |