Finite Group DatabasebetaFinite Group DatabasebetaOrder 30600.
144 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 57 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 |
|---|---|---|
| 5. C2×D3825 | C2 | semidirect |
| 6. C4×C9×C17×C25 | C2 | semidirect |
| 11. C9×C17×C25 | D4 | semidirect |
| 18. C4×C17×C25 | D9 | semidirect |
| 26. C4×C9×C25 | D17 | semidirect |
| 32. C4×C9×C17 | D25 | semidirect |
| 38. C17×C25 | D36 | semidirect |
| 48. C9×C25 | D68 | semidirect |
| 56. C9×C17 | D100 | semidirect |
| 64. C4×C25 | D153 | semidirect |
| 71. C4×C17 | D225 | semidirect |
| 80. C4×C9 | D425 | semidirect |
| 85. C25 | D612 | semidirect |
| 91. C17 | D900 | semidirect |
| 97. C9 | D1700 | semidirect |
| 103. C4 | D3825 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D5100 | 3 |
| D3060 | 5 |
| C2×D3825 | 2 |
| C4×C9×C17×C25 | 2 |
| D900 | 17 |