Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
326 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 326 conjugacy classes of subgroups — too many to draw. Only its 104 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×C3×C5×Dic6 | C2 | semidirect |
| 3. C2×C3×C3⋊#168 | C2 | semidirect |
| 4. C3×#6655 | C2 | direct (N × H) |
| 6. C2×#6655 | C3 | direct (N × H) |
| 11. C3×C5×Dic6 | C22 | semidirect |
| 14. C3×C3⋊#168 | C22 | semidirect |
| 17. C2×C5×Dic6 | C2×C3 | semidirect |
| 21. C2×C3⋊#168 | C2×C3 | semidirect |
| 24. #6655 | C2×C3 | direct (N × H) |
| 33. C2×C3×Dic6 | D5 | semidirect |
| 47. C5×Dic6 | C22×C3 | semidirect |
| 54. C3⋊#168 | C22×C3 | semidirect |
| 58. C2×C32×C5 | SD16 | semidirect |
| 71. C3×Dic6 | C2×D5 | semidirect |
| 94. C2×Dic6 | C3×D5 | semidirect |
| 99. C32×C5 | C2×SD16 | semidirect |
| 117. C2×C3×C5 | #214 | semidirect |
| 118. C2×C3×C5 | C3×SD16 | semidirect |
| 141. Dic6 | C2×C3×D5 | semidirect |
| 151. C2×C32 | #688 | semidirect |
| 158. C3×C5 | C2×#214 | semidirect |
| 159. C3×C5 | C2×C3×SD16 | semidirect |
| 177. C2×C5 | C3×#214 | semidirect |
| 180. C32 | C2×#688 | semidirect |
| 194. C2×C3 | #6655 | direct (N × H) |
| 195. C2×C3 | C3×#688 | semidirect |
| 198. C5 | C2×C3×#214 | semidirect |
| 206. C3 | C2×#6655 | direct (N × H) |
| 207. C3 | C2×C3×#688 | semidirect |
| 209. C2 | C3×#6655 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C5×Dic6 | 2 |
| C2×C32×D20 | 2 |
| C2×C3×C3⋊#168 | 2 |
| C3×#6655 | 2 |
| C2×C3×#688 | 3 |
| C2×#6655 | 3 |
| C2×C3×#214 | 5 |