Finite Group DatabasebetaFinite Group DatabasebetaOrder 11008.
492 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 127 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. #19135571 | C2 | semidirect |
| 4. C4×#13063235 | C2 | semidirect |
| 5. #19133049 | C2 | semidirect |
| 7. C43×#1567 | C2 | semidirect |
| 10. #14583297 | C4 | semidirect |
| 11. #14583272 | C4 | semidirect |
| 12. #14583250 | C4 | semidirect |
| 13. #14583246 | C4 | semidirect |
| 140. C8×C43 | #104 | semidirect |
| 165. #1567 | D43 | semidirect |
| 192. C43 | #9851 | semidirect |
| 307. C8 | #13063251 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19145154 | 2 |
| #19135571 | 2 |
| #19135422 | 2 |
| C4×#13063235 | 2 |
| #19133049 | 2 |
| #19133045 | 2 |
| C43×#1567 | 2 |
| #9851 | 43 |