Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
710 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 710 conjugacy classes of subgroups — too many to draw. Only its 159 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. C22×C5×C3⋊Dic3 | C2 | semidirect |
| 2. C2×C3×#1220 | C2 | semidirect |
| 3. C2×#67158 | C2 | semidirect |
| 4. C2×#67157 | C2 | semidirect |
| 5. #10624229 | C2 | direct (N × H) |
| 6. C2×#67154 | C2 | semidirect |
| 12. C2×C5×C3⋊Dic3 | C22 | semidirect |
| 13. C3×#1220 | C22 | semidirect |
| 15. #67158 | C22 | semidirect |
| 16. #67157 | C22 | semidirect |
| 17. #67154 | C22 | semidirect |
| 19. C2×#1220 | D3 | semidirect |
| 37. C22×C3⋊Dic3 | D5 | semidirect |
| 47. #1220 | C2×D3 | semidirect |
| 63. C2×C32×C5 | #41 | semidirect |
| 76. C2×C3⋊Dic3 | C2×D5 | semidirect |
| 107. C32×C5 | C2×#41 | semidirect |
| 131. C2×C3×C5 | #237 | semidirect |
| 162. C2×C32 | #709 | semidirect |
| 172. C3×C5 | C2×#237 | semidirect |
| 190. C2×C5 | #3805 | semidirect |
| 193. C32 | C2×#709 | semidirect |
| 209. C2×C3 | #6779 | semidirect |
| 212. C5 | C2×#3805 | semidirect |
| 222. C3 | C2×#6779 | semidirect |
| 225. C2 | #10624229 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C5×C3⋊Dic3 | 2 |
| C2×C3×#1220 | 2 |
| C2×#67158 | 2 |
| C2×#67157 | 2 |
| #10624229 | 2 |
| C2×#67154 | 2 |
| C2×#6779 | 3 |
| C2×#3805 | 5 |