Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
636 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 123 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. C4×#13063240 | C2 | semidirect |
| 4. #19132714 | C2 | semidirect |
| 5. C4×#100×C43 | C2 | semidirect |
| 7. C22×(C2×D43)⋊C4 | C4 | semidirect |
| 14. #14582771 | C4 | semidirect |
| 15. #14582754 | C4 | semidirect |
| 17. C4×C22⋊Dic43 | C4 | semidirect |
| 18. #14582687 | C4 | semidirect |
| 71. C23×D43 | C42 | semidirect |
| 109. C22⋊Dic43 | C42 | semidirect |
| 217. C4×#100 | D43 | semidirect |
| 247. C43 | #12622 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19137249 | 2 |
| C2×#14582687 | 2 |
| C4×#13063240 | 2 |
| #19132714 | 2 |
| C4×#100×C43 | 2 |
| #12622 | 43 |