Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
538 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 538 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. #19134672 | C2 | semidirect |
| 5. #19132504 | C2 | semidirect |
| 6. #19132448 | C2 | semidirect |
| 7. C43×#1826 | C2 | semidirect |
| 10. #14583217 | C4 | semidirect |
| 11. #14583212 | C4 | semidirect |
| 54. C22⋊(C43⋊C8) | C2×C4 | semidirect |
| 67. C2×C4⋊C4×C43 | C2×C4 | semidirect |
| 68. C2×C4⋊C4×C43 | C2×C4 | semidirect |
| 226. #1826 | D43 | semidirect |
| 262. C43 | #9525 | semidirect |
| 279. C2×C4⋊C4 | C4×D43 | semidirect |
| 280. C2×C4⋊C4 | C4×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19144535 | 2 |
| #19137360 | 2 |
| #19134672 | 2 |
| #19133125 | 2 |
| #19132504 | 2 |
| #19132448 | 2 |
| C43×#1826 | 2 |
| #9525 | 43 |