Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
468 conjugacy classes of subgroups; only the 232 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 232 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. C2×C5×Q8×C9 | C2 | semidirect |
| 2. C5×Q8×D9 | C2 | direct (N × H) |
| 4. C2×C5×Dic18 | C2 | semidirect |
| 7. C5×Q8×C9 | C22 | semidirect |
| 11. C5×Dic18 | C22 | semidirect |
| 12. C2×Q8×D9 | C5 | direct (N × H) |
| 18. C2×C5×D9 | Q8 | direct (N × H) |
| 23. C2×Q8×C9 | C2×C5 | semidirect |
| 24. Q8×D9 | C2×C5 | direct (N × H) |
| 26. C2×Dic18 | C2×C5 | semidirect |
| 34. C2×C5×C9 | C2×Q8 | semidirect |
| 36. C5×D9 | C2×Q8 | direct (N × H) |
| 39. C2×C5×Q8 | D9 | direct (N × H) |
| 42. Q8×C9 | C22×C5 | semidirect |
| 46. Dic18 | C22×C5 | semidirect |
| 56. C5×C9 | C22×Q8 | semidirect |
| 59. C5×Q8 | C2×D9 | direct (N × H) |
| 64. C2×D9 | C5×Q8 | direct (N × H) |
| 83. C2×C9 | C2×C5×Q8 | semidirect |
| 85. D9 | C2×C5×Q8 | direct (N × H) |
| 88. C2×Q8 | C5×D9 | direct (N × H) |
| 97. C2×C5 | Q8×D9 | direct (N × H) |
| 99. C9 | C22×C5×Q8 | semidirect |
| 102. Q8 | C2×C5×D9 | direct (N × H) |
| 109. C5 | C2×Q8×D9 | direct (N × H) |
| 117. C2 | C5×Q8×D9 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C5×Q8×C9 | 2 |
| C5×Q8×D9 | 2 |
| C2×C4×C5×D9 | 2 |
| C2×C5×Dic18 | 2 |
| C2×C5×D3×Q8 | 3 |
| C2×Q8×D9 | 5 |