Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
3798 conjugacy classes of subgroups; only the 387 normal subgroups are shown.
This group has 3798 conjugacy classes of subgroups — too many to draw. Only its 387 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. C2×#14583055 | C2 | semidirect |
| 3. #19134530 | C2 | semidirect |
| 6. C22×#10621885 | C22 | semidirect |
| 9. C2×#13063249 | C22 | semidirect |
| 46. C24×C43 | Q16 | semidirect |
| 105. C22×C43 | #451 | semidirect |
| 136. C43 | #32882 | semidirect |
| 164. C24 | #10621885 | semidirect |
| 222. C22 | #14583055 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583055 | 2 |
| #19142882 | 2 |
| #19134530 | 2 |
| #19134505 | 2 |
| C24×Q8×C43 | 2 |
| #32882 | 43 |