Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
216 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 93 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. #19153111 | C2 | semidirect |
| 2. #19153108 | C2 | semidirect |
| 3. #19153106 | C2 | semidirect |
| 4. #19153102 | C2 | semidirect |
| 5. #19153099 | C2 | semidirect |
| 6. #19153099 | C2 | semidirect |
| 7. #19153098 | C2 | semidirect |
| 8. #19153096 | C2 | semidirect |
| 9. #19153091 | C2 | semidirect |
| 10. #19153091 | C2 | semidirect |
| 12. #19153078 | C2 | semidirect |
| 13. C4×C22⋊D179 | C2 | semidirect |
| 14. #19153071 | C2 | semidirect |
| 15. C22⋊Q8×C179 | C2 | semidirect |
| 103. C179 | #542 | semidirect |
| 115. C22⋊Q8 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153111 | 2 |
| #19153108 | 2 |
| #19153106 | 2 |
| #19153102 | 2 |
| #19153099 | 2 |
| #19153098 | 2 |
| #19153096 | 2 |
| #19153091 | 2 |
| #19153086 | 2 |
| #19153078 | 2 |
| C4×C22⋊D179 | 2 |
| #19153071 | 2 |
| C22⋊Q8×C179 | 2 |
| #542 | 179 |