Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
1602 conjugacy classes of subgroups; only the 275 normal subgroups are shown.
This group has 1602 conjugacy classes of subgroups — too many to draw. Only its 275 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. #19134672 | C2 | semidirect |
| 4. #19134670 | C2 | semidirect |
| 5. #19134668 | C2 | semidirect |
| 6. #342×D43 | C2 | semidirect |
| 7. C43×#1820 | C2 | semidirect |
| 10. C2×C4×D172 | C4 | semidirect |
| 11. C2×#13063287 | C4 | semidirect |
| 32. C22×C4×D43 | C2×C4 | semidirect |
| 36. C2×C4⋊Dic43 | C2×C4 | semidirect |
| 42. C2×(C2×D43)⋊C4 | C2×C4 | semidirect |
| 46. C2×C4×Dic43 | C2×C4 | semidirect |
| 50. C2×C4⋊C4×C43 | C2×C4 | semidirect |
| 53. C2×C42×C43 | C2×C4 | semidirect |
| 157. #1820 | D43 | semidirect |
| 182. C43 | #20689 | semidirect |
| 198. C2×C4⋊C4 | C4×D43 | semidirect |
| 211. C2×C42 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583373 | 2 |
| #19137172 | 2 |
| #19134672 | 2 |
| #19134670 | 2 |
| #19134668 | 2 |
| #342×D43 | 2 |
| C43×#1820 | 2 |
| #20689 | 43 |