Finite Group DatabasebetaFinite Group DatabasebetaOrder 11456.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 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. #19153106 | C2 | semidirect |
| 2. #19153106 | C2 | semidirect |
| 3. #19153099 | C2 | semidirect |
| 4. #19153097 | C2 | semidirect |
| 5. #19153096 | C2 | semidirect |
| 6. #19153095 | C2 | semidirect |
| 7. #19153092 | C2 | semidirect |
| 8. #19153090 | C2 | semidirect |
| 10. C4×C22⋊D179 | C2 | semidirect |
| 11. (C22⋊D179)⋊C4 | C2 | semidirect |
| 12. #19153072 | C2 | semidirect |
| 13. #19153069 | C2 | semidirect |
| 14. C2×C22⋊Dic179 | C2 | semidirect |
| 15. C2×C22⋊C4×C179 | C2 | semidirect |
| 16. C2×Dic358 | C22 | semidirect |
| 22. C2×C4×D179 | C22 | semidirect |
| 23. C4⋊Dic179 | C22 | semidirect |
| 24. C4⋊Dic179 | C22 | semidirect |
| 25. C4⋊Dic179 | C22 | semidirect |
| 26. Dic179⋊C4 | C22 | semidirect |
| 27. Dic179⋊C4 | C22 | semidirect |
| 28. Dic179⋊C4 | C22 | semidirect |
| 29. Dic179⋊C4 | C22 | semidirect |
| 30. Dic179⋊C4 | C22 | semidirect |
| 38. (C2×D179)⋊C4 | C22 | semidirect |
| 39. (C2×D179)⋊C4 | C22 | semidirect |
| 40. (C2×D179)⋊C4 | C22 | semidirect |
| 41. C4×Dic179 | C22 | semidirect |
| 42. C4×Dic179 | C22 | semidirect |
| 43. C4×Dic179 | C22 | semidirect |
| 110. C179 | #551 | semidirect |
| 126. C2×C22⋊C4 | D179 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19153106 | 2 |
| #19153099 | 2 |
| #19153097 | 2 |
| #19153096 | 2 |
| #19153095 | 2 |
| #19153092 | 2 |
| #19153090 | 2 |
| #19153082 | 2 |
| C4×C22⋊D179 | 2 |
| (C22⋊D179)⋊C4 | 2 |
| #19153072 | 2 |
| #19153069 | 2 |
| C2×C22⋊Dic179 | 2 |
| C2×C22⋊C4×C179 | 2 |
| #551 | 179 |