Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
844 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. C2×#14582685 | C2 | semidirect |
| 3. #19134587 | C2 | semidirect |
| 4. C4×#99×C43 | C2 | semidirect |
| 5. C23×D172 | C4 | semidirect |
| 13. #14582759 | C4 | semidirect |
| 14. #14582754 | C4 | semidirect |
| 53. #99×C43 | D4 | semidirect |
| 195. C4×C43 | AΣL(1,𝔽16) | semidirect |
| 200. C4×#99 | D43 | semidirect |
| 225. C43 | #13221 | semidirect |
| 257. #99 | D172 | semidirect |
| 400. C4 | #14582685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19137951 | 2 |
| C2×#14582685 | 2 |
| #19134587 | 2 |
| C4×#99×C43 | 2 |
| #13221 | 43 |