Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1434 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1434 conjugacy classes of subgroups — too many to draw. Only its 275 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. #19135771 | C2 | direct (N × H) |
| 3. C2×#14582665 | C2 | semidirect |
| 4. C2×C43×#543 | C2 | semidirect |
| 10. #14582665 | C22 | semidirect |
| 12. C43×#543 | C22 | semidirect |
| 15. C24×D43 | Q8 | semidirect |
| 20. C22×C22⋊D43 | Q8 | semidirect |
| 23. C23×Dic43 | Q8 | semidirect |
| 54. C23×D43 | C2×Q8 | semidirect |
| 77. C22×Dic43 | C2×Q8 | semidirect |
| 157. C2×#543 | D43 | semidirect |
| 167. C2×C43 | #2032 | semidirect |
| 172. #543 | C2×D43 | semidirect |
| 180. C43 | C2×#2032 | semidirect |
| 329. C2 | #19135771 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#13063239 | 2 |
| #19135771 | 2 |
| C2×#14582665 | 2 |
| C2×C43×#543 | 2 |
| C2×#2032 | 43 |