Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
332 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 4. #19132771 | C2 | semidirect |
| 5. #19132769 | C2 | semidirect |
| 6. #19132755 | C2 | semidirect |
| 7. C43×#1407 | C2 | semidirect |
| 8. #14583510 | C4 | semidirect |
| 10. #14583273 | C4 | semidirect |
| 11. #14583264 | C4 | semidirect |
| 17. #14582961 | C4 | semidirect |
| 35. #13063317 | C2×C4 | semidirect |
| 54. C4×C43⋊C8 | C2×C4 | semidirect |
| 57. C4⋊Q8×C43 | C2×C4 | semidirect |
| 61. #97×C43 | C2×C4 | semidirect |
| 164. #1407 | D43 | semidirect |
| 190. C43 | #13607 | semidirect |
| 198. C4⋊Q8 | C4×D43 | semidirect |
| 224. #97 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145662 | 2 |
| #19136285 | 2 |
| #19136263 | 2 |
| #19132771 | 2 |
| #19132769 | 2 |
| #19132755 | 2 |
| C43×#1407 | 2 |
| #13607 | 43 |