Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
278 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 80 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. C32×Q8×D5 | C2 | semidirect |
| 3. C3×#6718 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. C3×#6662 | C2 | semidirect |
| 6. C3×#6656 | C2 | semidirect |
| 7. C3×#6649 | C2 | semidirect |
| 9. #91513 | C3 | direct (N × H) |
| 23. C3×Q8×D5 | D3 | semidirect |
| 24. C3×Q8×D5 | C2×C3 | semidirect |
| 28. #6718 | C2×C3 | semidirect |
| 29. C5×#215 | C2×C3 | semidirect |
| 34. #6662 | C2×C3 | semidirect |
| 35. #6656 | C2×C3 | semidirect |
| 36. #6649 | C2×C3 | semidirect |
| 50. C3×#215 | D5 | semidirect |
| 84. Q8×D5 | C3×D3 | semidirect |
| 134. #215 | C3×D5 | semidirect |
| 136. C32×C5 | #137 | semidirect |
| 209. C3×C5 | #942 | semidirect |
| 210. C3×C5 | C3×#137 | semidirect |
| 233. C32 | #4061 | semidirect |
| 253. C5 | C3×#942 | semidirect |
| 262. C3 | #91513 | direct (N × H) |
| 263. C3 | C3×#4061 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×Q8×D5 | 2 |
| C3×#6772 | 2 |
| C3×#6718 | 2 |
| C3×C5×#215 | 2 |
| C3×#6662 | 2 |
| C3×#6656 | 2 |
| C3×#6649 | 2 |
| C3×#4061 | 3 |
| #91513 | 3 |
| C3×#942 | 5 |