Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
706 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 706 conjugacy classes of subgroups — too many to draw. Only its 175 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. #19132424 | C2 | semidirect |
| 4. #19132423 | C2 | semidirect |
| 5. C43×#1274 | C2 | semidirect |
| 11. #14582950 | C4 | semidirect |
| 14. C4×#10621872 | C4 | semidirect |
| 40. C4×C43⋊C8 | C2×C4 | semidirect |
| 47. C4×C8×C43 | C2×C4 | semidirect |
| 69. C42×C43 | M16 | semidirect |
| 82. C4×Dic43 | M16 | semidirect |
| 137. #1274 | D43 | semidirect |
| 157. C43 | #7855 | semidirect |
| 182. C4×C8 | C4×D43 | semidirect |
| 218. C42 | #10621872 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143223 | 2 |
| #376×D43 | 2 |
| #19132424 | 2 |
| #19132423 | 2 |
| C43×#1274 | 2 |
| #7855 | 43 |