Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
688 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 688 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 |
|---|---|---|
| 2. #19143054 | C2 | semidirect |
| 3. #19136245 | C2 | semidirect |
| 4. #19134563 | C2 | semidirect |
| 5. #19132723 | C2 | semidirect |
| 6. #19132715 | C2 | semidirect |
| 7. C43×#2128 | C2 | semidirect |
| 9. C2×#13063351 | C4 | semidirect |
| 10. C22×#10621882 | C4 | semidirect |
| 18. #14582903 | C4 | semidirect |
| 19. #14582893 | C4 | semidirect |
| 50. C2×#10621877 | C2×C4 | semidirect |
| 51. C22×C43⋊C8 | C2×C4 | semidirect |
| 70. C22×D4×C43 | C2×C4 | semidirect |
| 79. #117×C43 | C2×C4 | semidirect |
| 252. #2128 | D43 | semidirect |
| 289. C43 | #13102 | semidirect |
| 303. C22×D4 | C4×D43 | semidirect |
| 324. #117 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143861 | 2 |
| #19143054 | 2 |
| #19136245 | 2 |
| #19134563 | 2 |
| #19132723 | 2 |
| #19132715 | 2 |
| C43×#2128 | 2 |
| #13102 | 43 |