Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1538 conjugacy classes of subgroups; only the 297 normal subgroups are shown.
This group has 1538 conjugacy classes of subgroups — too many to draw. Only its 297 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. #123×Dic43 | C2 | semidirect |
| 3. #19135009 | C2 | semidirect |
| 4. #19134878 | C2 | semidirect |
| 6. #99×Dic43 | C2 | semidirect |
| 14. C22×C4×Dic43 | C22 | semidirect |
| 19. #14582774 | C22 | semidirect |
| 20. #14582762 | C22 | semidirect |
| 23. C22⋊C4×Dic43 | C22 | semidirect |
| 24. #14582665 | C22 | semidirect |
| 27. C43×#458 | C4 | semidirect |
| 71. #123×C43 | C2×C4 | semidirect |
| 75. #99×C43 | C2×C4 | semidirect |
| 93. C22×C4×C43 | C22×C4 | semidirect |
| 112. C22⋊C4×C43 | C22×C4 | semidirect |
| 195. Dic43 | #458 | direct (N × H) |
| 218. #458 | Dic43 | direct (N × H) |
| 230. C43 | C4×#458 | semidirect |
| 242. #123 | C2×Dic43 | semidirect |
| 272. #99 | C2×Dic43 | semidirect |
| 310. C22×C4 | C22×Dic43 | semidirect |
| 323. C22⋊C4 | C22×Dic43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(5,𝔽2)×Dic43 | 2 |
| #123×Dic43 | 2 |
| #19135009 | 2 |
| #19134878 | 2 |
| #19134543 | 2 |
| #99×Dic43 | 2 |
| C2×C43×#458 | 2 |
| C4×#458 | 43 |