Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
880 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 880 conjugacy classes of subgroups — too many to draw. Only its 95 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 |
|---|---|---|
| 1. #19143622 | C2 | semidirect |
| 3. #19134516 | C2 | semidirect |
| 4. #19132931 | C2 | semidirect |
| 5. #19132502 | C2 | semidirect |
| 6. #19132500 | C2 | semidirect |
| 7. C43×#1783 | C2 | semidirect |
| 33. C2×#10621877 | D4 | semidirect |
| 69. C2×M16×C43 | D4 | semidirect |
| 168. C22×D43 | #100 | semidirect |
| 243. #1783 | D43 | semidirect |
| 277. C43 | #9503 | semidirect |
| 293. C2×M16 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143622 | 2 |
| #19137945 | 2 |
| #19134516 | 2 |
| #19132931 | 2 |
| #19132502 | 2 |
| #19132500 | 2 |
| C43×#1783 | 2 |
| #9503 | 43 |