Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
768 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 768 conjugacy classes of subgroups — too many to draw. Only its 147 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. #19132716 | C2 | semidirect |
| 4. #19132715 | C2 | semidirect |
| 5. C43×#1391 | C2 | semidirect |
| 7. C22×#10621872 | C4 | semidirect |
| 8. C2×M16×D43 | C4 | semidirect |
| 13. #14582871 | C4 | semidirect |
| 15. #99×D43 | C4 | semidirect |
| 16. #14582867 | C4 | semidirect |
| 18. #14582865 | C4 | semidirect |
| 35. C2×#10621877 | C2×C4 | semidirect |
| 41. C22×C43⋊C8 | C2×C4 | semidirect |
| 51. #13063240 | C2×C4 | semidirect |
| 58. C2×M16×C43 | C2×C4 | semidirect |
| 59. C22×C8×C43 | C2×C4 | semidirect |
| 62. #99×C43 | C2×C4 | semidirect |
| 209. #1391 | D43 | semidirect |
| 234. C43 | #12577 | semidirect |
| 254. C2×M16 | C4×D43 | semidirect |
| 257. C22×C8 | C4×D43 | semidirect |
| 271. #99 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #410×D43 | 2 |
| #19143037 | 2 |
| #19132716 | 2 |
| #19132715 | 2 |
| C43×#1391 | 2 |
| #12577 | 43 |