Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
672 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 89 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. #19136270 | C2 | semidirect |
| 5. #19132725 | C2 | semidirect |
| 6. #19132715 | C2 | semidirect |
| 7. C43×#2123 | C2 | semidirect |
| 9. C2×#13063356 | C4 | semidirect |
| 10. C22×#10621884 | C4 | semidirect |
| 18. #14582903 | C4 | semidirect |
| 19. #14582893 | C4 | semidirect |
| 49. C2×#10621877 | C2×C4 | semidirect |
| 50. C22×C43⋊C8 | C2×C4 | semidirect |
| 70. C22×Q8×C43 | C2×C4 | semidirect |
| 79. #117×C43 | C2×C4 | semidirect |
| 247. #2123 | D43 | semidirect |
| 282. C43 | #13100 | semidirect |
| 290. C22×Q8 | C4×D43 | semidirect |
| 317. #117 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143870 | 2 |
| #19143054 | 2 |
| #19136270 | 2 |
| #19134566 | 2 |
| #19132725 | 2 |
| #19132715 | 2 |
| C43×#2123 | 2 |
| #13100 | 43 |