Finite Group DatabasebetaFinite Group DatabasebetaOrder 2624.
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. #13050157 | C2 | semidirect |
| 2. #13050157 | C2 | semidirect |
| 3. #13050150 | C2 | semidirect |
| 4. #13050148 | C2 | semidirect |
| 5. #13050147 | C2 | semidirect |
| 6. #13050146 | C2 | semidirect |
| 7. #13050143 | C2 | semidirect |
| 8. #13050141 | C2 | semidirect |
| 10. C4×C22⋊D41 | C2 | semidirect |
| 11. #13050124 | C2 | semidirect |
| 12. #13050123 | C2 | semidirect |
| 13. #13050120 | C2 | semidirect |
| 14. C2×C22⋊Dic41 | C2 | semidirect |
| 15. C2×C22⋊C4×C41 | C2 | semidirect |
| 24. C2×C4×D41 | C22 | semidirect |
| 25. C2×Dic82 | C22 | semidirect |
| 37. #10620281 | C22 | semidirect |
| 38. #10620281 | C22 | semidirect |
| 39. #10620281 | C22 | semidirect |
| 40. C4⋊Dic41 | C22 | semidirect |
| 41. C4⋊Dic41 | C22 | semidirect |
| 42. C4⋊Dic41 | C22 | semidirect |
| 43. #10620279 | C22 | semidirect |
| 44. #10620279 | C22 | semidirect |
| 45. #10620279 | C22 | semidirect |
| 46. #10620279 | C22 | semidirect |
| 47. #10620279 | C22 | semidirect |
| 48. C4×Dic41 | C22 | semidirect |
| 49. C4×Dic41 | C22 | semidirect |
| 50. C4×Dic41 | C22 | semidirect |
| 111. C41 | #551 | semidirect |
| 126. C2×C22⋊C4 | D41 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13050157 | 2 |
| #13050150 | 2 |
| #13050148 | 2 |
| #13050147 | 2 |
| #13050146 | 2 |
| #13050143 | 2 |
| #13050141 | 2 |
| #13050133 | 2 |
| C4×C22⋊D41 | 2 |
| #13050124 | 2 |
| #13050123 | 2 |
| #13050120 | 2 |
| C2×C22⋊Dic41 | 2 |
| C2×C22⋊C4×C41 | 2 |
| #551 | 41 |