Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
312 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 60 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. #10624287 | C2 | semidirect |
| 2. #10624205 | C2 | semidirect |
| 3. C3×#6717 | C2 | semidirect |
| 4. C3×C5×#215 | C2 | semidirect |
| 5. #10623800 | C2 | semidirect |
| 6. #10623799 | C2 | semidirect |
| 7. #10623797 | C2 | semidirect |
| 11. C32×C5×Q8 | C22 | semidirect |
| 13. C4⋊(C3⋊D15) | C22 | semidirect |
| 19. C3×C3⋊#168 | C22 | semidirect |
| 20. C3×C5×C3⋊C8 | C22 | semidirect |
| 28. #6717 | D3 | semidirect |
| 32. C5×#215 | D3 | semidirect |
| 49. C3×#215 | D5 | semidirect |
| 56. C3×C5×Q8 | C2×D3 | semidirect |
| 57. C3×C5×Q8 | C2×D3 | semidirect |
| 77. C3⋊#168 | C2×D3 | semidirect |
| 79. C5×C3⋊C8 | C2×D3 | semidirect |
| 95. C32×Q8 | C2×D5 | semidirect |
| 104. C3×C3⋊C8 | C2×D5 | semidirect |
| 134. #215 | D15 | semidirect |
| 141. C32×C5 | AGL(1,ℤ/8) | semidirect |
| 143. C5×Q8 | D32 | semidirect |
| 178. C3×Q8 | D3×D5 | semidirect |
| 179. C3×Q8 | C2×D15 | semidirect |
| 201. C3⋊C8 | C2×D15 | semidirect |
| 223. C3×C5 | #914 | semidirect |
| 224. C3×C5 | #914 | semidirect |
| 251. C32 | #4060 | semidirect |
| 253. Q8 | D3×D15 | semidirect |
| 276. C5 | #63941 | semidirect |
| 286. C3 | #91506 | semidirect |
| 287. C3 | #91803 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10624287 | 2 |
| #10624205 | 2 |
| C3×#6717 | 2 |
| C3×C5×#215 | 2 |
| #10623800 | 2 |
| #10623799 | 2 |
| #10623797 | 2 |
| #91803 | 3 |
| #91506 | 3 |
| #63941 | 5 |