Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
730 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 730 conjugacy classes of subgroups — too many to draw. Only its 117 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. #19133263 | C2 | semidirect |
| 5. #19132497 | C2 | semidirect |
| 6. #19132496 | C2 | semidirect |
| 7. C43×#1545 | C2 | semidirect |
| 45. C4⋊(C43⋊C8) | D4 | semidirect |
| 62. C4⋊C8×C43 | D4 | semidirect |
| 194. #1545 | D43 | semidirect |
| 222. C43 | #9397 | semidirect |
| 254. C4⋊C8 | C22⋊D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19143618 | 2 |
| #19139542 | 2 |
| #19134584 | 2 |
| #19133263 | 2 |
| #19132497 | 2 |
| #19132496 | 2 |
| C43×#1545 | 2 |
| #9397 | 43 |