Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
504 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 99 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. #19143651 | C2 | semidirect |
| 3. C2×#14582632 | C2 | semidirect |
| 4. #19132956 | C2 | semidirect |
| 5. #19132482 | C2 | semidirect |
| 6. #19132438 | C2 | semidirect |
| 7. C43×#1504 | C2 | semidirect |
| 9. #14583232 | C4 | semidirect |
| 11. #14583215 | C4 | semidirect |
| 14. #14583049 | C4 | semidirect |
| 16. #14583032 | C4 | semidirect |
| 238. #1504 | D43 | semidirect |
| 280. C43 | #9264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145356 | 2 |
| #19143651 | 2 |
| C2×#14582632 | 2 |
| #19132956 | 2 |
| #19132482 | 2 |
| #19132438 | 2 |
| C43×#1504 | 2 |
| #9264 | 43 |