Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1164 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 1164 conjugacy classes of subgroups — too many to draw. Only its 205 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. #19147997 | C2 | semidirect |
| 3. #19135773 | C2 | semidirect |
| 4. #19135772 | C2 | semidirect |
| 5. #19135771 | C2 | semidirect |
| 6. #19134326 | C2 | semidirect |
| 7. C43×#2032 | C2 | semidirect |
| 29. C22×Dic86 | Q8 | semidirect |
| 30. C22×C22⋊D43 | Q8 | semidirect |
| 32. C23×Dic43 | Q8 | semidirect |
| 34. C22×C4×D43 | Q8 | semidirect |
| 187. #2032 | D43 | semidirect |
| 212. C43 | #23474 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19147997 | 2 |
| C2×#14582871 | 2 |
| #19135773 | 2 |
| #19135772 | 2 |
| #19135771 | 2 |
| #19134326 | 2 |
| C43×#2032 | 2 |
| #23474 | 43 |