Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
864 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 864 conjugacy classes of subgroups — too many to draw. Only its 147 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. #19135424 | C2 | semidirect |
| 2. C4×#13063252 | C2 | semidirect |
| 3. #19133187 | C2 | semidirect |
| 4. #19133034 | C2 | semidirect |
| 15. Q82×C43 | C4 | semidirect |
| 18. C43×#555 | C4 | semidirect |
| 20. C43×#550 | C4 | semidirect |
| 135. Q8×C43 | #104 | semidirect |
| 200. Q82 | Dic43 | semidirect |
| 203. #555 | Dic43 | semidirect |
| 205. #550 | Dic43 | semidirect |
| 220. C43 | #8441 | semidirect |
| 330. Q8 | #13063252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19135424 | 2 |
| C4×#13063252 | 2 |
| #19133187 | 2 |
| #19133034 | 2 |
| C43×#3483 | 2 |
| #8441 | 43 |