Finite Group DatabasebetaFinite Group DatabasebetaOrder 15104.
2590 conjugacy classes of subgroups; only the 747 normal subgroups are shown.
This group has 2590 conjugacy classes of subgroups — too many to draw. Only its 747 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. C23×D472 | C2 | semidirect |
| 2. C22×#14273668 | C2 | direct (N × H) |
| 3. C23×C59⋊C16 | C2 | semidirect |
| 4. C23×D8×C59 | C2 | semidirect |
| 7. C22×D472 | C22 | semidirect |
| 8. C2×#14273668 | C22 | direct (N × H) |
| 9. C22×C59⋊C16 | C22 | semidirect |
| 12. C22×D8×C59 | C22 | semidirect |
| 18. C2×D472 | C23 | semidirect |
| 19. #14273668 | C23 | direct (N × H) |
| 20. C2×C59⋊C16 | C23 | semidirect |
| 26. C2×D8×C59 | C23 | semidirect |
| 41. D8×C59 | C24 | semidirect |
| 45. D472 | C24 | semidirect |
| 46. C59⋊C16 | C24 | semidirect |
| 49. C23×C59 | D16 | semidirect |
| 64. C22×C59 | C2×D16 | semidirect |
| 71. C23×D8 | D59 | semidirect |
| 75. C2×C59 | C22×D16 | semidirect |
| 83. C22×D8 | C2×D59 | semidirect |
| 87. C59 | C23×D16 | semidirect |
| 98. C2×D8 | C22×D59 | semidirect |
| 117. D8 | C23×D59 | semidirect |
| 125. C23 | #14273668 | direct (N × H) |
| 139. C22 | C2×#14273668 | direct (N × H) |
| 145. C2 | C22×#14273668 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×D472 | 2 |
| C22×#14273668 | 2 |
| C23×C59⋊C16 | 2 |
| C23×D8×C59 | 2 |
| C23×D16 | 59 |