Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 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 |
|---|---|---|
| 1. #19153108 | C2 | semidirect |
| 2. #19153106 | C2 | semidirect |
| 3. #19153103 | C2 | semidirect |
| 4. #19153099 | C2 | semidirect |
| 5. #19153098 | C2 | semidirect |
| 6. #19153095 | C2 | semidirect |
| 7. #19153091 | C2 | semidirect |
| 9. C4×Dic358 | C2 | semidirect |
| 10. C4×D716 | C2 | semidirect |
| 11. C4×C22⋊D179 | C2 | semidirect |
| 12. C4×C22⋊D179 | C2 | semidirect |
| 13. #19153070 | C2 | semidirect |
| 14. C42×D179 | C2 | semidirect |
| 15. #117×C179 | C2 | semidirect |
| 103. C179 | #529 | semidirect |
| 118. #117 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153108 | 2 |
| #19153106 | 2 |
| #19153103 | 2 |
| #19153099 | 2 |
| #19153098 | 2 |
| #19153095 | 2 |
| #19153091 | 2 |
| #19153086 | 2 |
| C4×Dic358 | 2 |
| C4×D716 | 2 |
| C4×C22⋊D179 | 2 |
| #19153070 | 2 |
| C42×D179 | 2 |
| #117×C179 | 2 |
| #529 | 179 |