Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
626 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 113 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. #19143618 | C2 | semidirect |
| 3. #19134584 | C2 | semidirect |
| 4. #19133021 | C2 | semidirect |
| 5. #19133019 | C2 | semidirect |
| 6. #19132453 | C2 | semidirect |
| 7. C43×#1286 | C2 | semidirect |
| 56. C4×C43⋊C8 | D4 | semidirect |
| 65. C4×C8×C43 | D4 | semidirect |
| 209. #1286 | D43 | semidirect |
| 236. C43 | #9485 | semidirect |
| 274. C4×C8 | D172 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143618 | 2 |
| #19139497 | 2 |
| #19134584 | 2 |
| #19133021 | 2 |
| #19133019 | 2 |
| #19132453 | 2 |
| C43×#1286 | 2 |
| #9485 | 43 |