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×D944 | C2 | direct (N × H) |
| 3. C23×C16×C59 | C2 | semidirect |
| 6. C22×D472 | C22 | semidirect |
| 7. C2×D944 | C22 | direct (N × H) |
| 9. C22×C16×C59 | C22 | semidirect |
| 14. C2×D472 | C23 | semidirect |
| 15. D944 | C23 | direct (N × H) |
| 19. C2×C16×C59 | C23 | semidirect |
| 30. D472 | C24 | semidirect |
| 31. C16×C59 | C24 | semidirect |
| 32. C23×C59 | D16 | semidirect |
| 43. C22×C59 | C2×D16 | semidirect |
| 51. C23×C16 | D59 | semidirect |
| 52. C2×C59 | C22×D16 | semidirect |
| 60. C22×C16 | C2×D59 | semidirect |
| 61. C59 | C23×D16 | semidirect |
| 71. C2×C16 | C22×D59 | semidirect |
| 83. C16 | C23×D59 | semidirect |
| 86. C23 | D944 | direct (N × H) |
| 96. C22 | C2×D944 | direct (N × H) |
| 101. C2 | C22×D944 | 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×D944 | 2 |
| C23×C16×C59 | 2 |
| C23×D16 | 59 |