Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
2222 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2222 conjugacy classes of subgroups — too many to draw. Only its 667 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 |
|---|---|---|
| 1. #19140555 | C2 | direct (N × H) |
| 2. C2×#14582828 | C2 | semidirect |
| 3. C2×#14582823 | C2 | semidirect |
| 5. C2×#14582797 | C2 | semidirect |
| 6. C2×C43×#376 | C2 | semidirect |
| 12. #14582828 | C22 | semidirect |
| 13. #14582823 | C22 | semidirect |
| 15. #14582797 | C22 | semidirect |
| 18. C43×#376 | C22 | semidirect |
| 112. C2×#376 | D43 | semidirect |
| 113. C2×C43 | #2644 | semidirect |
| 128. #376 | C2×D43 | semidirect |
| 132. C43 | C2×#2644 | semidirect |
| 219. C2 | #19140555 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19140555 | 2 |
| C2×#14582828 | 2 |
| C2×#14582823 | 2 |
| C2×#14582801 | 2 |
| C2×#14582797 | 2 |
| C2×C43×#376 | 2 |
| C2×#2644 | 43 |