Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
528 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 528 conjugacy classes of subgroups — too many to draw. Only its 131 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. #19147607 | C2 | semidirect |
| 2. #19136858 | C2 | semidirect |
| 3. #19136856 | C2 | semidirect |
| 4. #19136656 | C2 | semidirect |
| 5. #19136650 | C2 | semidirect |
| 6. #19136629 | C2 | semidirect |
| 7. #19136503 | C2 | semidirect |
| 8. #19136458 | C2 | semidirect |
| 9. C4×D16×C43 | C2 | semidirect |
| 153. C4×D16 | D43 | semidirect |
| 184. C43 | #33970 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147607 | 2 |
| #19136858 | 2 |
| #19136856 | 2 |
| #19136656 | 2 |
| #19136650 | 2 |
| #19136629 | 2 |
| #19136503 | 2 |
| #19136458 | 2 |
| C4×D16×C43 | 2 |
| #33970 | 43 |