Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
608 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 608 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 |
| 79. C24×C43 | C4⋊C4 | semidirect |
| 114. C22⋊C4×C43 | C4⋊C4 | semidirect |
| 282. AΣL(1,𝔽16) | Dic43 | semidirect |
| 286. C43 | #12960 | semidirect |
| 338. C24 | C4⋊Dic43 | semidirect |
| 393. C22⋊C4 | C4⋊Dic43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19137736 | 2 |
| #19135004 | 2 |
| #19134878 | 2 |
| #19134807 | 2 |
| #19132719 | 2 |
| #19132714 | 2 |
| C2×C43×AΣL(1,𝔽16) | 2 |
| #12960 | 43 |